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XYLENE POWER LTD.

FNR FUEL BUNDLES

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

INTRODUCTION:
Assembled fuel bundles are shipped to and from FNR sites. Practical shipping 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 fuel bundles. Each fixed octagonal fuel bundle is an assembly of 416 vertical fuel tubes. Each square fuel bundle is an assembly of 280 vertical fuel tubes. A practical fast neutron reactor (FNR) is an assembly of alternating octagonal and square fuel bundles. In the core zone the square fuel bundles are mobile. 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 in reusable sealed lead containers each weighing about 50 tonnes.
 

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 aat 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 expands 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)

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 a 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 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 additional axles and forward wheels to assist with 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 weight constraints relating to practical road transport of highly radioactive fuel bundles in lead containers of sufficient wall thickness for certain biosafety.

Each fuel tube bottom plug has a tapered bottom tip for easy downward vertical fuel tube insertion into the fuel bundle. The fuel tube bottom plugs also have 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.
 

FUEL BUNDLE ASSEMBLY 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 X 6 m high. 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.

Each square fuel bundle is initially less than 11.875 inches X 11.875 inches face to face X 6 m high. Below the mobile square fuel bundles are hydraulic actuators, positioned by the steel lattice, which support the mobile fuel bundles and set the amount of mobile fuel bundle insertion into the rigid matrix of fixed fuel bundles.

The fuel bundle shroud, diagonal sheet 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.
 

DEFINITIONS:
Active fuel tube:
Each active fuel tube contains 2 X 0.35 m long core fuel rods where nuclear fission occurs, 3 X ~ 0.60 m blanket fuel rods above the core fuel rods, 3 X ~ 0.60 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 allowance for the two welded end plugs.

Passive fuel tube:
Contains 7 X ~ 0.60 m long blanket fuel rods which absorb neutrons plus liquid sodium

Shroud:
Fuel bundle shrouds are fabricated from (3 / 16) inch thick HT-9 steel sheet. 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. 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 fixed position passive fuel bundle contains only passive fuel tubes, blanket fuel rods and some sodium.

Fuel Bundle Components:
Each fuel bundle has 4 shroud side panels, 4 corner girders, 2 diagonal sheets, (1 / 16) inch diameter fuel tube spacer rods, a bottom grating, and a bottom filter. The top diagonal sheet intersection potentially provides a fuel bundle lifting point.

A hydraulic actuator for a mobile square fuel bundle consists of a 1.5 m long hydraulic cylinder 10.75 inch OD + piston + 1.5 m hydraulic cylinder which moves a mobile fuel bundle up and down, is located in the open steel lattice. In the core zone each hydraulic cylinder has a fitting near its base that mates with the corresponding hydraulic pressure line.
 

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 array of simple 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. 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

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 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 fixed 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) 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 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 reactor core region the fuel bundle shroud sheets and diagonal reinforcing sheets contain narrow vertical slots in the reactor core region to allow shroud and diagonal sheet swelling in the core region without causing overall horizontal fuel bundle 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 power 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.
 

FIXED OCTAGONAL FUEL BUNDLES:
Consists of a shroud surrounding 416 fixed position fuel tubes. The 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:
Consists of 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.

The mobile fuel bundles have bottom probes that extend 1.5 m below the fuel tubes. these probes have pointed bottom tips that mate with corresponding conical holes in the actuator piston. About 0.5 m below the bottom of the fuel tubes is a sphere mounted on the probe. The OD of this sphere slides inside the ID of the hydraulic cylinder. The purpose of the sphere is to hold the mobile fuel bundle vertical while in the fully retracted position before its surrounding octagonal fuel bundles are installed. Once the octagonal fuel bundes are in position and the mobile fuel bundle is partially inserted this ball is outside the hydraulic cylinder and no longer has a stabilizing function.

The actuator piston housing has a hole through its side near its top. The purpose of this hole is to release hydraulic pressure when the mobile fuel bundle reaches its maximum insertion position. This hole prevents the piston being accidentally driven out of its cylinder.
 

FUEL BUNDLE ARRARY ASSEMBLY AND DISASSEMBLY:

In assembly of the fuel bundle array the mobile fuel bundles are ALWAYS installed before their surrounding fixed fuel bundles. Similarly, in disassembly of the fuel bundle array the fixed fuel bundles are ALWAYS removed before moving 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 operation the liquid sodim temperature at the open steel lattice is likely to be about 160 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 160 deg C X 13.125 inch = 0.042 inch
The fuel bundle leg sockets must provide sufficient play to accommodate 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 fuel tube 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 and spacing must accommodate this swelling. To achieve certain cool shutdown the fully swollen mobile fuel bundles must 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 can linearly swell due to fast neutron bombardment without the external width of the fuel bundle changing. Fuel bundles are intended to be replaced after 15% linear swelling of the most intensely neutron irradiated fuel tube sections. The fuel tube array center-to-center spacing is established by the fuel bundle bottom grating and by the (1 / 16) inch diameter spacer rods that are located out of the main fast neutron flux and hence are protected from fast neutron induced swelling.

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 with respect to one another and hence rocking laterally as might occur during an earthquake. A key issue is the washer like swelling allowance spacer that goes on this bolt between the adjacent fixed fuel bundles. This spacer allows a modest amount of core zone swelling without the mobile fuel bundles jamming so as not to be able to reliably slide vertically up and down. Increasing the length of each such spacer increases the swelling allowance but decreases the average fuel concentration in both the core and blanket zones. Note that the sockets into which the legs of the fixed fuel bundles plug must be designed for the same swelling allowance.
 

EARTHQUAKE PROTECTION:
The primary sodium pool is supported by layer of ball bearings located at the outside bottom of the primary sodium pool. The steel assembly supporting the primary sodium pool is 26 m diameter and is slightly bowled. The bottom of the primary sodium pool is also slightly bowled with maximum depth at its center chosewn to safely absorb up to 3 g of earthquake sourced horizontal ground acceleration.

Above each active mobile fuel bundle is a 4.5 m long indicator tube. For ease of fuel bundle transportation the indicator tubes are hooked to the mobile fuel bundle lifting points after the fuel bundle is installed at the FNR site.
 

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 may also act as passive fuel bundles.
 

INDICATOR TUBE:
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 vertical flow of liquid sodium through the indicator tube. The indicator tube has hollow walls which in addition to providing thermal insulation also provide positive buoyancy so that when 1.5 m of the indicator tube is projecting above the primary liquid sodium surface it maintains a firm upright connection to the corresponding mobile fuel bundle. The hollow walls also provide a gamma ray propagation path through the 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 height of the top of its indicator tube above the primary liquid sodium surface.

An indicator tube is connected to each active mobile square fuel bundle after the fuel bundle is horizontally positioned and is disconnected before that fuel bundle is relocated.

Each indicator tube: is sufficiently buoyant to keep it upright, 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 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 TUBE ATTACHMENT:
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 attachment point is the fuel bundle central lifting point. Once the indicator tubes are in place the fire suppression floats are slipped between them. The indicator tubes should be thin wall for buoyancy to keep each 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.

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_______________

(Consider use of thinner wall material)
 

STEEL SUPPORT LATTICE:
The 1.5 m high open steel support lattice supports the entire weight of the fuel bundles and 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 push tube 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 about 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 top bolts and then lifting the fixed fuel bundle a few inches using the overhead gantry crane.

Note that the open steel lattice at the bottom of the primary liquid sodium pool will thermally expand with increasing surrounding liquid sodium temperature. During normal operation the liquid sodim temperature at the open steel lattice is likely to be about 160 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 160 deg C X 13.125 inch = 0.042 inch
The U clamps must provide sufficient play to accommodate differential thermal expansion.
 

MECHANICAL CONSIDERATIONS:
A major issue in fuel bundle design is horizontal mechanical stability and rigidity because the overall fuel bundle height of 7.5 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. 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 grid. The center junction of the diagonal sheets provides a lifting point for fuel bundle installation and removal and to allow use of bolts for connecting together adjacent fixed octagonal fuel bundles.
 

The corner girders of the fixed fuel bundles transfer the weight of the fuel tubes onto the fixed octagonal fuel bundle legs. These legs extend 1.5 m below the fuel tubes 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.

In operation each mobile fuel bundle's weight is borne by the 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 height of the steel lattice and at the top by a hydraulic actuator vent hole.

The hydraulic actuator for a square mobile fuel bundle consists of a 1.5 m long hydraulic cylinder 10.75 inch OD + piston + which moves a mobile square fuel bundle up and down, is located in the open steel lattice. Each hydraulic actuator has a fitting which mates with the corresponding hydraulic pressure line.

The fuel tube spacing within a fuel bundle is maintained using horizontal (1 / 16) inch diameter steel rods that run between the fuel tubes at about 0.8 m, 2.0 m, 4.0 m and 6.0 m from the fuel tube bottom. The (1 / 16) inch diameter east-west rods are sufficiently vertically separated from the (1 / 16) inch diameter north-south rods to avoid significant obstruction of the upward natural primary liquid sodium flow.

The fuel bundle mechanical design must tolerate longitudinal swelling of the steel components of the fuel bundle that are exposed to fast neutrons. For example the shroud sheets contain vertical slots in the core fuel zone so that the material can expand in width without warping. Longitudinal swelling of the corner girders should balance longitudinal swelling of the shroud sheets.
 

NUCLEAR DESCRIPTION:
A practical FNR consists of a variable thickness pancake shaped inner core completely surrounded by a > 1.3 m thick neutron absorption blanket. The fission chain reaction occurs primarily in the middle core where the core fuel rods of the fixed and mobile fuel bundles overlap. Excess neutrons originating in the middle core fuel are absorbed by U-238 in the upper amd lower core zones and in the blanket. The middle 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 the reactor must be subcritical. This fuel bundle design constraint enables safe octagonal fuel bundle transport and 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 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 power. 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 DETAIL:
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 1.5 m long probe from the fuel tube bottom to the piston. This probe holds the mobile fuel bundle vertical when the bundle is fully retracted. It also stabilizes the fuel bundle input filter.

The probe has a stabilizing sphere which fits inside 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 blind insertion into the 10.75 inch OD, 9.75 inch ID X 1.5 m high steel pipe that acts as a 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 fuel bundle control portion 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 sodiumpool 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 7800 lb of lifting force to raise the mobile fuel bundle and its indicator tube. If the piston attempts top 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.
 

FUEL BUNDLE FILTERS:
At the bottom of each fuel bundle is a filter supported by the cross plates. The purpose of the 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 completely block 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. For the mobile square fuel bundles the diagonals from the push tube 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 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. 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.
 

FUEL BUNDLE STRENGTH CALCULATIONS:
ACTIVE FUEL BUNDLES:
Each fixed fuel bundle is structurally stabilized by its rigid outer corner double angle girders, shroud plates and diagonal sheets. These corner girders are each:
(1 / 2) inches thick X 7.5 m. The cross sectional area of each of these double angle girders is:
= 1.8047 inch^2

Each 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 TUBE SUPPORT GRATINGS:
The fuel tubes in a fuel bundle are held in position by the steel grating 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.
 

FUEL BUNDLE LIFTING:
The central lifting point for a fuel bundle is attached to 0.25 inch _______thick diagonal plates. The corner girders of the octagonal fuel bundles must project further upwards to allow for bolting to other fixed fuel bundles at the top of the girders. The diagonal plates connecting each fuel bundle lifting point to the corresponding fuel bundle corner girders must also allow unobstructed primary liquid sodium flow and must not prevent individual fuel tube insertion or extraction.

The indicator tubes must have bottom hooks that attach to the central lifting points of the mobile square fuel bundles.
 

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___________

Each fixed octagonal fuel bundle contains 416 fuel tubes, each with a mass of 7.4 kg________. Hence the mass of fuel tubes is:
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 fuel bundle shroud and the outer corner girders which form the fixed fuel bundle legs. Immediately below the fuel tubes 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 shroud and outer corner girders and then to either the actuator piston via diagonal plates or to the adjacent fixed fuel bundles while still permitting unobstructed primary liquid sodium flow. The diagonal plates connecting the piston push tube 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.
 

HYDRAULIC ACTUATOR COMPONENTS:
There is a 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
 

ULTRASONIC IMAGING SYSTEM:
A very important accessory required for installation and removal of fuel bundles is an ultrasonic imaging system that allows the gantry crane operator to "see" inside the liquid sodium pool. This imaging system is required to easily and accurately position the fuel bundles, to seal the connection between the hydraulic line and the active fuel bundle control portion actuator, to add and remove the indicator tube, to hook onto the fuel bundle for lifting and to address other mechanical issues under the liquid sodium surface. When performing these operations the liquid sodium should be cooled to about 120 degrees C to minimize thermal stress on the ultrasonic imaging apparatus.
 

TOTAL OCTAGONAL BUNDLE + SQUARE BUNDLE CROSS SECTIONAL AREA ALLOCATION:
The total area allocation for this pair of fuel bundles is:
(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 (7.75 m / 2) X 9.8 m / s^2 = 74,035 N-m
= 74,035 N-m X (1 inch / 0.0254 m) X 1 lb / (.454 k g X 9.8 m / s^2)
= 655,122 inch-lbs
which permits one end of a single fuel bundle to be picked up by a crane.
 

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 the mobile bundles should be installed in the withdrawn position before the installing the corresponding surrounding fixed fuel bundles. Similarly the fixed fuel bundles surrounding a mobile bundle should be extracted from the primry sodium pool before extracting the corresponding withdrawn 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. We need to develop a simple means of ensuring that the fuel bundle insertion and extraction orders are always correct.
 

REQUIRED EARTHQUAKE TRANSVERSE TORQUE RESISTANCE:
If the fuel bundles are not further stress relieved the fixed fuel bundle torque resistance must be large enough to resist the torque caused by the combined fixed plus mobile fuel bundle mass of:
3899.152 kg + 2517.16 kg = 6416.3 kg
acting at a distance of:
1.5 m + 1.8 m + 0.9 m = 4.2 m

With a 1 g transverse acceleration the torque is:
6416.3 kg X 9.8 m / s^2 X 4.2 m = 264,095 N - m
= 264,095 N - m X (1 inch / 0.0254 m) X 1 lb / (0.454 kg X 9.8 m / s^2)
= 2,336,927 inch lbs.

In an extreme earthquake which causes a 3 g ground acceleration this theoretical transverse torque could reach 7 million inch-lbs.

This transverse torque can be reduced many fold by supporting the assembly of fuel bundles on a layer of ball bearings so that during an earthquake the ground can move while the assembly of fuel bundles remains almost stationary due to its inertial mass.
 

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
 

ACCELERATION PROTECTION WITHOUT BALL BEARING SUPPORT:
As shown above, a 1 g horizontal acceleration produces a transverse torque of:
2,336,927 inch lbs.

Hence, without the ball bearing support system this fuel assembly provides working torque protection against earthquakes with up to:
(1,103,336 inch-lbs / 2,336,927 inch lbs) X 1 g = 0.472 g
horizontal ground acceleration.
 

BALL BEARING SUPPORT:
One way of relieving the large transverse torque potentially caused by a severe earthquake is to keep the primary liquid sodium pool nearly stationary while the ground moves underneath it. Assume that the torque load is reduced 10X by suspending the entire primary sodium pool on ball bearings. Then the maximum torque load reduces to:
(7,000,000 inch-lbs) / 10 = 700,000 inch-lb
which is well below the equipment design working torque.

An important issue in earthquake protection is bolting the fixed fuel bundles together to form a rigid matrix. We do not want liquid sodium sloshing back and forth to change the fuel assembly geometry and hence its reactivity.
 

This web page last updated May 31, 2020

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