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XYLENE POWER LTD.

FNR FUEL BUNDLES

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

INTRODUCTION:
This web page develops the dimensions of FNR fuel bundles expressed in intergral multiples of (1 / 16) inch, (5 / 8) inch and in metres for use on various drawings and in nuclear calculations.

In order to enable siting practical Fast Neutron Reactors (FNRs) in urban areas fully assembled FNR fuel tube bundles (AKA Fuel Bundles) should be shipped as finished modules to and from FNR sites. Practical fuel bundle shipping by road imposes a limit on the weight of the shielded shipping container and hence on the fuel bundle dimensions.

The design of FNR fuel tube bundles is complicated by the necessity for insertion, relocation and removal of individual fuel bundles immersed in a liquid sodium pool which is at a temperature of about 120 degrees C.

Each fuel bundle consists of a vertically elongated basket that contains either 248 or 384 sealed 0.500 inch OD X 6.001 m long chrome steel fuel tubes. Each such basket has a crane lifting point on top and has a bottom support.

An important aspect of fuel bundles is the chimney effect which stabilizes the natural circulation flow of primary liquid sodium coolant. In essence the reactor core zone acts as a constant 460 degree C source of primary liquid sodium. The reactor thermal power is proportional to the primary liquid sodium flow rate and the primary liquid sodium temperature differential. The temperature differential also establishes the primary liquid sodium flow rate due to the decrease in sodium density with increasing temperature. Were viscous effects not present the reactor thermal power would be proportional to the square of the temperature differential. However, viscous flow resistance tends to linearize the relationship between reactor thermal power and primary sodium temperature differential.

In order to maximize the fuel to coolant ratio in the FNR core zone while allowing sufficient internal storage of inert gases the fuel tube wall thickness is chosen to be 0.035 inch.

A fuel bundle basket is usually replaced at the time when its contained fuel tubes are reprocessed.

It is contemplated that the reactor core fuel rods are initially:
38 X (5 / 8) inch = 23.75 inch = 0.60325 m long,
the top and bottom blanket fuel rod stacks are each
113 X (5 / 8) inch = 70.625 inch = 1.793875 m long
and these rods and rod stacks are contained in vertical steel tubes positioned laterally on a square grid:
1 X (5 / 8) inch = 0.625 inch = 0.015875 m center-to-center.

In order to enable reactor temperature setpoint change via controlled adjustment of adjacent fuel bundle core rod overlap each fuel bundle has an overall length of:
504 X (5 / 8) inch = 315.000 inch = 8.0010 m.

In order to meet the fuel bundle transportation weight constraints the fuel bundle widths are small compared to their height.

Each fuel bundle must be sufficiently robust that a crane can lift one end of the fuel bundle to rotate it from axis horizontal to axis vertical without the fuel bundle deforming due to its own weight. The corresponding fuel bundle bending torque withstand capability implies a fuel bundle capacity to withstand transverse accelerations of about 0.5 g when the fuel bundle is vertical and is only bottom supported.

Each fuel bundle basket is formed from shroud plates, diagonal plates, corner girders, adapter plates, a grating and a bottom support that are designed to collectively provide the required bending torque resistance.

The bending torque transferred to individual fuel tubes is minimized by external wire windings on every second fuel tube which fix the inter-fuel tube gap along the fuel tube lengths and which stabilize the fuel tube positions with respect to the fuel bundle corner girders, shroud plates and diagonal plates.

In order to achieve good liquid sodium natural circulation, which requires fuel tubes on a square grid, and good fuel assembly structural stability, alternating wider fixed and narrower movable fuel bundles are used. The wider fixed fuel bundles are corner connected to form a rigid matrix that is centrally mounted in a deep liquid sodium pool. The narrower movable fuel bundles slide vertically between adjacent wider fixed fuel bundles to provide local reactivity adjustment and hence local reactor temperature setpoint control.

The movable fuel bundles enter the matrix of fixed fuel bundles from the bottom to ensure reactor shutdown by gravity on loss of reactor control power.

The different fuel bundle widths require different physical support arrangements.

The entire assembly of fuel bundles is supported by an open steel lattice that rests on a layer of low friction ball bearings.

In an earthquake the fuel assembly remains nearly stationary due to its inertia and low friction mount while the primary sodium pool structure moves with the surrounding ground. The relative motion of the pool structure with respect to the contained primary liquid sodium causes primary sodium pool surface waves. However, the wave troughs must reach more than 6 m below the normal liquid sodium surface level before they can even touch the top of the fuel bundles. Hence this reactor design is highly earthquake resistant.
 

DEFINITIONS:
Active Fuel Tube:
An active fuel tube contains one 0.6 m long core fuel rod where nuclear fission occurs, a stack of 5 X 0.36 m blanket fuel rods above the core fuel rod, a stack of 5 X 0.36 m blanket fuel rods below the core fuel rod and sufficient liquid sodium for good thermal coupling between the fuel rods and the fuel tube inner wall.

Passive fuel tube:
Each passive fuel tube contains 12 X 0.36 m long blanket fuel rods which absorb neutrons plus sufficient liquid sodium for good thermal coupling between the fuel rods and the fuel tube inner wall.

The passive fuel tubes in movable fuel bundles also contain 1.0 m long X (3 / 8) inch diameter steel rods to keep the blanket rods at the correct height when the movable passive fuel bundles are in the fully withdrawn position.

Active Fuel Bundle:
An Active Fuel Bundle is a fuel bundle composed of Active Fuel Tubes

Passive Fuel Bundle:
A Passive Fuel Bundle is a fuel bundle composed of passive fuel tubes.

In order to achieve fuel bundle mounting interchangability the Passive Fuel Bundles are made and mounted in the same manner as the Active Fuel Bundles. However, the movable Passive Fuel Bundles always remain in their fully withdrawn position.
 

FUEL BUNDLE FEATURES
1) A practical FNR contains alternating fixed and movable fuel bundles in a chequer board pattern.

2) Each fixed fuel bundle is an ~ 3.6 tonne assembly containing 384 fuel tubes of which 212 are unwound and 172 have external spiral windings for tube spacing control.

3) Each movable fuel bundle is an ~ 2.4 tonne assembly containing 248 fuel tubes of which 136 are unwound and 112 have a external spiral windings for tube spacing control.

4) In the active portion of the reactor each movable fuel bundles can be moved up and down by a dedicated hydraulic actuator. The active portion of the reactor 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 fuel bundles. The fuel bundles are transported one at a time on trucks or rail cars in reusable sealed transport containers each weighing about 80 tonnes.

5) Each fuel bundle has three sections, a lower support section, a grating and fuel tube mid-section and a lifting point upper section.

6) A fixed fuel bundle has:
94 X (5 / 8) inch = 58.75 inch = 1.49225 m
high legs that support the bottom of the grating above the top surface of the open steel lattice. These legs are actually lower extenions of the fuel bundle corner girders which are reinforced with supplementary diagonal interleg bracing. The middle:
391 X (5 / 8) inch = 244.375 inch = 6.207125 m
of each fuel bundle contains the fuel tubes and grating and is strengthened by diagonal plates, shroud plates and corner girders. The top:
19 X (5 / 8) inch = 11.875 inch = 0.301625 m
is an upper extension of the mid-section that provides a central lifting point and that provides for top corner connection to adjacent fixed fuel bundles.

7) For movable fuel bundles there is a
(504 - 13 - 391 - 2) X (5 / 8) inch
= 98 X (5 / 8) inch = 61.25 inch = 1.55575 m
long 8 inch schedule 160 (8.625 inch OD, 6.813 inch ID) steel support pipe. When the movable fuel bundle is fully inserted into the fixed fuel bundle matrix the length of this support pipe remaining in the hydraulic cylinder is:
6 X (5 / 8) inch = 3.75 inch = 0.09525 m

The length
(98 - 24 - 6) X (5 / 8) inch
= 68 X (5 / 8) inch = 42.5 inch = 1.0795 m is the maximum withdrawal of a movable fuel bundle from the matrix of fixed fuel bundles. The maximum length of support pipe within the 10 inch schedule 80 steel pipe (10.750 inch OD, 9.562 inch ID) which forms the hydraulic cylinder is:
(68 + 6) X (5 / 8) inch = 46.25 inch = 1.17475 m.

The top
24 X (5 / 8) inch = 15.000 inch = 0.381 m of the support pipe has welded on 1.000 inch thick radial adapter plates
26 X (5 / 8) inch = 16.25 inch = 0.41275 m high
that transfer the fuel bundle load on to the support pipe and that provide the required bending torque resistance. The adapter plates lie in the same plane as the diagonal plates. The adapter plates provide a:
2 X (5 / 8) inch = 1.25 inch = 0.03175 m
high gap between the top of the support pipe and the bottom of the grating to allow inward radial flow of liquid sodium over the top of the support pipe.

Below the adapter plates are tapered guides the purpose of which is to keep the top of the support pipe centered in the hydraulic cylinder when the moveable fuel bundle is fully retracted.

The bottom of the support pipe has an external machined taper the purpose of which is to assist in blind insertion of the support pipe into the hydraulic cylinder.

The piston in the hydraulic cylinder has a tapered top the purpose of which is to center the support pipe on the piston in the hydraulic cylinder. The maximum taper OD should be slightly less than the minimum support pipe ID.

When the movable fuel bundles are fully withdrawn the combination of centering the support pipe in the hydraulic cylinder at both its top and bottom should keep the movable fuel bundle straight upright and should permit its use to assist as a guide for blind insertion of adjacent fixed fuel bundles into their sockets.

8) The middle:
391 X (5 / 8) inch = 6.2071 m
of a movable fuel bundle contains the grating and fuel tubes and is strengthened by diagonal plates, shroud plates and corner girders.

9) The top:
13 X (5 / 8) inch = 8.125 inch = 0.206375 m
of a movable fuel bundle provides a central lifting point which is also used for attachment of an Indicator Tube.
 

FUEL BUNDLE MATERIAL:
1) Extensive metallurgical investigations have shown that FNR fuel tubes should be fabricated from HT-9 steel (86% Fe, 12% Cr, 1% Mo, 0% C, 0% Ni).

2) The fuel bundle basket material is the same HT-9 alloy that is used to make the fuel tubes. The reasons for using this alloy are the same as the reasons for using it to make fuel tubes.

3) The fuel tube height of 6.001 m is limited by the 20 foot length availability of 0.500 inch OD X 0.035 inch wall thickness HT-9 steel tube.
 

FUEL BUNDLE GEOMETRY:
1) In plan view the two different size fuel bundles fit together as shown below:

2) On the above diagram the fixed fuel bundles are shown in red and the movable fuel bundles are shown in blue. The solid purple at the fuel bundle corners indicates the fuel bundle corner girders. Yellow indicates fixed fuel bundle corner spacers which are 0.707 inch thick. This spacing and the corner attachments are realized with cast E fittings to prevent small parts accidentally falling into the fuel bundle baskets or falling to the primary sodium pool floor.

3) The ordinate parallel and abcissa parallel lines show the positions of the fuel bundle shroud plates. The diagonal lines show the positions of the fuel bundle diagonal plates, although the diagonal plate thickness is not to scale. The green lines are layout guide lines.

4) Only a few fuel tubes are shown to indicate how the fuel tubes fit into the fuel bundles with respect to adjacent shroud plates, diagonal plates and corner girders.

5) The maximum fuel bundle width is set by practical limits on the weight of a shielded container needed to transport an irradiated fuel bundle.

6) For bending torque resistance each fuel bundle has four vertical corner girders, two vertical interlocked internal diagonal plates, four vertical external shroud plates, one grating and two vertical interlocked adapter plates. The fuel tubes fit within the four nearly triangular spaces defined by the internal diagonal plates, the external shroud plates, the corner girders and the grating. The bottom of each fuel tubes is positioned and supported by a grating intersection. The grating is primarily supported by the adapter plates which are in the same vertical plane as are the diagonal plates.

7) The diagonal plates are interlocked, are internally welded to each other like dividers in a wine carton and are then are internally welded to the corner girders. However in the extended core zone, where fast neutron induced material swelling is anticipated, the diagonal plates are reduced in width by 12.5% and are not welded to the corner girders.

8) A bit of geometry shows that if the diagonal plates replace a diagonal line of wound fuel tubes the maximum possible thickness of a diagonal plate that runs between the unwound fuel tubes is:
[2 ((5 / 8)inch)^2]^0.5 - (1 / 2) inch = 0.3838 inch

9) However, for good fuel tube cooling we need to provide (1 / 16) inch wall clearance for each unwound fuel tube adjacent to a diagonal plate, so the maximum diagonal plate thickness reduces to:
(0.3838 inch - 2 (1 / 16) inch
= 0.3838 inch - 0.125 inch = 0.2588 inch

10) Thus the thickness of the fuel bundle diagonal plates should be:
0.25 inch
thick HT-9.

11) The top of the diagonal plates is at the top of the lifting point allowance. The height of the lifting point allowance is:
13 X (5 /8) inch = 8.125 inch = 0.206375 m

12) The bottom of the diagonal plates is at the top of the grating.

13) The vertical allowance for the assembled fuel tubes, end plugs, grating and differential swelling length expansion is:
391 X (5 / 8) inch = 244.375 inch = 6.207125 m

14) The grating height is:
5 X (5 / 8) inch = (25 / 8) inch =0.07935 m

15) Hence the height of the diagonal plates is:
((13 + 391 - 5) X (5 / 8) inch = 249.375 inch = 6.334125 m

16) The fuel tube spacing within a fuel bundle is maintained using a spiral (1 / 8) inch thick stranded wire winding on every second fuel tube and by the corner girders, shroud plates and diagonal plates.

17) The fixed fuel bundle corner girders are:
504 X (5 / 8) inch = 315.0 inch = 8.001 m long.

18) The fixed fuel bundle corner girder length allocated to top corner attachment to adjacent fixed fuel bundles, including tool clearance, is:
6 X (5 / 8) inch = 3.75 inch = 0.09525 m.

19)The remaining fixed fuel bundle leg length which extends below the grating bottom is:
(504 - 6 - 13 - 391) X (5 / 8) inch
= 94 X (5 / 8) inch = 58.75 inch = 1.49225 m.

20) The fuel bundle grating is supported by 1.000 inch thick adapter plates that are:
26 X (5 / 8) inch = 16.25 inch = 0.41275 m
high which transfer the fuel tube load to either the fixed fuel bundle corner girder legs or a movable fuel bundle support pipe. The adapter plates are positioned directly under the fuel bundle diagonal plates to minimize obstruction of vertical liquid sodium flow. Note that (3 / 8) inch are ground off the top edges to reduce the adapter plate top width to (1 / 4) inch.

21) The adapter plates of a movable fuel bundle must provide sufficient bending torque resistance. These plates provide a 1.25 inch gap between the top of the support pipe and the bottom of the grating to allow inward radial flow of liquid sodium over the top of the support pipe. These plates also provide a 1.25 inch high outside ledge to positively support the movable fuel bundle corner girders.

22) The vertical height of the movable fuel bundle adapter plates is limited by the requirement to provide sufficient movable fuel bundle withdrawal from the matrix of fixed fuel bundles. The extent of this withdrawal is limited to:
(94 - 26) X (5 / 8) inch = 68 X (5 / 8) inch = 42.5 inch = 1.0795 m.

23) Note that:
6 X (5 / 8) inch = 3.75 inch = 0.09525 m
of support pipe length remains in the hydraulic cylinder at maximum insertion of a movable fuel bundle into the matrix of fixed fuel bundles.

24) On movable fuel bundle adapter plates (1 / 2) inch is ground off each side of each vertical edge to properly mate with the movable fuel bundle corner girders.

25) The movable fuel bundle adapter plates each have a 2 X (5 / 8) inch high horizontal top extension that passes over the top of the support pipe and which directly supports the grating. Note that (3 / 8) inch are ground off the top edges.

26) On movable fuel bundles the corner girders extend from the top of the lifting point allowance to 1.25 inch above the bottom of the adapter plates. The adapter plates are welded on to the 8 inch schedule 160 support pipe so as to provide 2 X (5 / 8) inch clearance between the top of the support pipe and the bottom of the grating. The top edges of the adapter plate have (3 / 8) inch ground off to reduce the adapter plate thickness to (1 / 4) inch at the grating bottom.

27)For the movable fuel bundles the corner girder height is:
(13 + 391 + 26 - 2) X (5 / 8) inch = 428 X (5 / 8) inch
= 267.5 inch = 6.7945 m

28) The rectangular sheet metal enclosure around a fuel bundle is known as its shroud. The shroud provides part of the fuel bundle structural rigidity, positions and physically protects the fuel tubes and excludes particulate matter. The fuel bundle shroud is formed from (3 / 16) inch thick HT-9 sheet steel panels which are outside welded to the corner girders.

29) For the movable fuel bundle the top of the shroud plates is at the top of the corner girders.

30) For the movable fuel bundle the bottom of the shroud plates is at at the bottom of the corner girders.

31) For the movable fuel bundles the shroud plate height is:
428 X (5 / 8) inch = 267.5 inch = 6.7945 m

32) The top of the shroud plates for the fixed fuel bundles is at the top of the lifting point alloance.

33) The bottom of the shroud plates for the fixed fuel bundles is at the bottom of the adapter plates.

34) Hence the height of the shroud plates for the fixed fuel bundles is:
(13 + 391 + 26) X (5 / 8) inch = 430 X (5 / 8) inch = 268.75 inch = 6.82625 m.

35) Each fixed fuel tube bundle has a maximum outside width allowance including tolerances and clearance of:
[23 X (5 / 8) inch] = 14.375 inches
exterior face to exterior face, is 8.001 m high and contains 384 X 6.00075 m high fuel tubes.

36) The width of the fixed fuel bundle shroud plates is:
(23 - 6) X (5 / 8) inch = 10.625 inch = 0.269875 m

37) Each movable fuel tube bundle has a maximum outside width allowance including tolerances and clearance of:
[19 X (5 / 8) inch] = 11.875 inches
exterior face to exterior face, is 8.001 m high and contains 248 X 6.00075 m high fuel tubes.

38) The width of the movable fuel bundle shroud plates is:
(19 - 4) X (5 / 8) inch = 9.375 inch = 0.238125 m

39) In the fixed fuel bundles the width of the diagonal plates is:
2^0.5 X 18 X (5 / 8) inch = 13.9099 inch = 0.35331146 m

40) In the fixed fuel bundles the maximum width of the adapter plates is:
2^0.5 X 18 X (5 / 8) inch = 13.9099 inch = 0.35331146 m

41) In the movable fuel bundles the width of the diagonal plates is:
2^0.5 X 15 X (5 / 8) inch = 13.2583 inch = 0.33676082 m

42) In the movable fuel bundles the maximum width of the adapter plates is:
2^0.5 X 17 X (5 / 8) inch = 15.0260191 inch = 0.38166 m

43) To prevent overall fuel bundle swelling in the core region in that region the diagonal plates are reduced in width by 12.5% and the fuel bundle shroud sheets are not welded to the corner girders to allow both diagonal and shroud sheet swelling in the core region without causing overall horizontal fuel bundle width swelling.

44) Below the adapter plates the fixed fuel bundle legs are stabilized by diagonal cross bracing.

P>45) The legs of the fixed fuel bundles are corner girder lower extensions and fit into cast "E" sockets which are securely fastened to the 1.5 m high open steel lattice. The long axis of these sockets is parallel to the fuel bundle diagonal plates. The middile of the "E"socket is 0.707 inch thick inches for a theoretical movable fuel bundle shroud plate outside face to fixed fuel bundle shroud plate outside face separation of 0.75 inches.

46) The top corners of the fixed fuel bundles are connected to the top corners of the adjacent fixed fuel bundles by "E" sockets containing 0.707 inch middle spacers and (1 / 2) inch diameter through bolts to form a rigid matrix of fixed fuel bundles within which the movable fuel bundles slide vertically. The spacer thickness is 0.707 inches corresponds to a theoretical movable fuel bundle shroud plate outside face to fixed fuel bundle shroud plate outside face separation of 0.75 inches.

47) The crane lifting point of the movable fuel bundle is made from a
13 X (5 / 8) inch = 8.125 inch = 0.206375 m
diagonal plate extension above the maximum height of the tops of the fuel tube top plugs. The crane lifting point must be carefully designed to not over stress the diagonal plates.

48) Assume that the crane lifting point consists of four 2.0 inch diameter holes. There should be 4 inches of plate height above the holes and 2 inches of plate below the holes. With 2.0 inch diameter lifting pins, each hole can potentially lift:
2 inch X (1 /4) ich X 10,000 lb / inch^2 = 5000 lbs.

49) In normal reactor operation the movable fuel bundles are raised by hydraulic piston actuators which are held in position by the supporting open steel lattice. The actuators support the movable fuel bundles and limit the amount of insertion of each movable fuel bundle into the matrix of fixed fuel bundles. When the movable fuel bundles are fully withdrawn the hydraulic cylinders keep the movable fuel bundles upright. This arrangement involves minor vee notching of the bottom of the adapter plates.

50) The cross sectional area of each fixed fuel bundle corner girder is:
5 x (5 / 8) inch X (5 / 8) inch = 1.953125 inch^2

51) The cross sectional area of each movable fuel bundle corner girder is:
3 X (5 / 8) inch X (5 / 8) inch = 1.1719 inch^2

52) These dimensions result in a linear center to center distance between similar fuel bundles of:
[14.375 inch + 11.875 inch = 26.25 inch
= 26.25 inch X .0254 m / inch = 0.66675 m
Which allows easy drawing scaling using:
1 m = 1.5 (19 + 23) X (5 / 8) inch
or
1 m = 63 X (5 / 8) inch

53) For the fixed fuel bundles the shroud inside face to shroud inside face distance is:
21 X (5 / 8) inch + (1 / 8) inch = 13.250 inches.

54) For the movable fuel bundles the shroud plate inside face to shroud plate inside face distance is:
17 X (5 / 8) inch + (1 / 8) inch = 10.750 inchs.

55) Lifting hole radial position:
The total width of each diagonal plate in the movable fuel bundle is:
15 X (5 / 8) inch X 2^0.5 = 13.25825 inch

Hence the half plate width is:
13.25825 inch / 2 = 6.6 inch

56) Hence locate the axis of the lifting hole about 3.3 inch from the diagonal plate center.

57) Hence for the movable fuel bundle the distance from the diagonal plate center to the nearest perimeter of the lifting hole is:
3.3 inch - (2.0 inch / 2) = 2.3 inch.

58) WE NEED TO BE CONCERNED ABOUT THE LOCAL SHEER STRESS ON THE DIAGONAL PLATE NEAR THE LIFTING HOLE!
 

FUEL BUNDLE VERTICAL STRUCTURE:
1) The fuel tube height is set by FNR design calculations relating to the core height, blanket thickness and plenum height. This height is further constrained by material length availability.

2) In the fixed fuel bundle below the adapter plates open diagonal cross bracing is used to increase the legs bending torque resistance. In the case of the fixed fuel bundles the bottom of the legs must be square so as to fit into cast sockets mounted on the open steel lattice. There must also be sufficient open space through the cross bracing to allow lateral liquid sodium circulation.

3) An important issue in earthquake protection is fastening the fixed fuel bundles together at their top corners to form a rigid fixed fuel bundle matrix. It is important to prevent liquid sodium, which can slosh back and forth during an earthquake, from significantly changing the fuel assembly geometry and hence its reactivity.

4) In order to meet the bending torque resistance requirements the shroud plates and corner girders of movable fuel bundles must physically overlap the 8 inch schedule 160 support pipe (8.625 inch OD, 6.813 inch ID) support pipe by about:
22 X (5 / 8) inch = 13.75 inch

5) In the case of the movable fuel bundles the support pipe end tip must have a tapered end to assist in blind insertion into the hydraulic cylinder.
 

SECONDARY VERTICAL DIMENSIONS:
1) Fuel tube length:
378 X (5 / 8) inch = 236.25 inch = 6.00075 m

2) Fuel tube end plug length:
= 5 X (5 / 8) inch X 0.0254 m / inch = 0.079375 m

3) Fuel tube end plug penetration of fuel tube:
= 2 X (5/ 8) inch X0.0254 m / inch = 0.03175 m

4) Fuel tube end plug projection beyond the fuel tube:
= 3 X (5 / 8) inch X 0.0254 m / inch = 0.047625 m

5) Saw cut [(3 / 16) inch wide] penetration of bottom end plug:
= 2 X (5/ 8) inch X0.0254 m / inch = 0.03175 m

6) Grating height:
= 5 X (5 / 8) inch X.0254 m / inch = 0.079375 m

7) Assembled height of grating + fuel tube plugs + fuel tubes:
= (5 + 3 - 2 + 378 + 3) X (5 / 8) inch X 0.0254 m / inch
= (387) X (5 / 8) inch X 0.0254 m / inch
= 6.1436 m

8) Allowance for differential fuel tube length growth:
= (391 - 387) X (5 / 8) inch X 0.0254 m / inch
= (4) X (5 / 8) inch X 0.0254 m / inch
= 0.0635 m

9) Bottom end plug shoulder length:
= 1 X (5 / 8) inch X 0.0254 m / inch = 0.015875 m

10) Top end plug shoulder length = 2 (1 / 8) inch

11) Top end plug (3 / 8) inch OD machined section:
= 3 (5 / 8) inch - (2 / 8) inch = (13 / 8) inch

12) Top end plug (3 / 8) inch threaded length:
(13 / 8) inch - (1 / 8) inch = (12 / 8) inch

13) Fuel tube inside length:
= (378 - 4) X (5 / 8) inch X 0.0254 m / inch
= (374) X (5 / 8) inch X 0.0254 m / inch
= 5.93725 m

14) Five Rod Blanket Stack:
113 X (5 / 8) inch X 0.0254 m / inch = 1.7939 m

15) Core Rod:
38 X (5 / 8) inch X0.0254 m / inch = 0.60325 m

16) Plenum:
(374 - 113 - 38 - 113) X (5 / 8) inch X 0.0254 m / inch
= 110 X (5 / 8) inch X 0.0254 m / inch
= 1.74625 m

17) Recall that lifting point vertical allowance ia:
13 X (5 / 8) inch = 8.125 inch

18) Lifting hole = 2.00 inch diameter
Hence we can have 4.125 inch of (1 / 4) inch steel plate above the lifting hole and 2.000 inch of clearance below the lifting hole.
 

SUMMARY OF COMPONENT VERTICAL DIMENSIONS:
Fixed Fuel Bundle Corner Girders = 504 X (5 / 8) inch
Fixed Fuel Bundle Corner Bolting Girder Extension = 6 X (5 / 8) inch
Fixed Fuel Bundle Crane Lift Point Allocation = 13 X (5 / 8) inch
Fixed Fuel Bundle Fuel Tube, Grating, Plug and Differential Expansion Allowance
= 391 X (5 / 8) inch
Grating Height = 5 X (5 / 8) inch
Diagonal Plate Height = (13 + 391 - 5) X (5 / 8) inch
= 399 X (5 / 8) inch
Fixed Fuel Bundle Adapter Plate Height = 26 X (5 / 8) inch
Fixed Fuel Bundle Shroud Plate Height:
(13 + 391 + 26) X (5 / 8) inch
= 430 X (5 / 8) inch
Fixed Fuel Bundle Leg Length Below Grating
= (504 - 6 - 13 - 391) X (5 / 8) inch
= 94 X (5 / 8) inch
End plug overall height = 5 X (5 / 8) inch
End plug penetration of fuel tube = 2 X (5 / 8) inch
Fuel tube = 378 X (5 / 8) inch
Active fuel tube Blanket rod stack = 113 X (5 / 8) inch
Core rods = 38 X (5 / 8) inch
Active fuel tube Plenum = 110 X (5 / 8) inch
 

Movable Fuel Bundle Crane Lift Point Allowance = 13 X (5 / 8) inch
Movable Fuel Bundle Fuel Tube, Grating, Plug, Space Allowance
391 X (5 / 8) inch
Grating = 5 X (5 / 8) inch
Diagonal Plate Height
= (13 + 391 - 5) X (5 / 8) inch
= 399 X (5 / 8) inch
Movable Fuel Bundle Adapter Plate Height = 26 X (5 / 8) inch

Movable Fuel Bundle Corner Girders = (13 + 391 + 24) X (5 / 8) inch
= 428 X (5 / 8) inch
= (13 + 391 + 26) X (5 / 8) inch
= 430 X (5 / 8) inch
Movable Fuel Bundle Shroud Plate Height:
(13 + 391 + 26) X (5 / 8) inch
= 428 X (5 / 8) inch
Support Pipe to Grating Gap = 2 X (5 / 8) inch
Movable Fuel Bundle Support Pipe Length
= (504 - 13 - 391 - 2) X (5 / 8) inch
= 98 X (5 / 8) inch

Fuel:
Active Fuel Tube Blanket Rod Stack = 113 X (5 / 8) inch
Core Rod = 38 X (5 / 8) inch
Active Fuel Tube Plenum = 110 X (5 / 8) inch
 

FUEL TUBE SPACING:
1) The fuel tube OD and ID are in part constrained by material availability.

2) The EBR-2 reactor had fuel tubes that were positioned on staggered centers. A staggered cemter 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 staggered center fuel bundle design is that as the fuel tubes swell over time the liquid sodium coolant passages become severely restricted, requiring mechanical pumping of the primary liquid sodium to maintain sufficient primary liquid sodium flow for reactor cooling.

3) To maintain sufficient primary liquid sodium flow by natural circulation the fuel tubes are positioned on a square grid so that the liquid sodium coolant passages between the fuel tubes remain open in the presence of fuel tube swelling. A square grid lends itself to square fuel bundles that have good reactor power modulation characteristics. However, a problem with a simple array of identical square fuel bundles is that the array lacks horizontal mechanical structural stability, especially in earthquake conditions.

4) In order to achieve both good liquid sodium natural circulation, which requires fuel tubes on a square grid, and good horizontal structural stability alternating movable and fixed fuel bundles of different sizes are used. Fixed fuel bundles are wider than movable fuel bundles, act as slide guides for movable fuel bundles and require different support arrangements than movable fuel bundles.

5) Within each fuel bundle the fuel tube bottoms are positioned by 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 12.5% 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.

6) Each fuel tube bottom plug has 3 /16 inch wide cross cuts for mating with the fuel bundle bottom grating which is formed from (1 / 8) inch thick steel sheet. The fuel tube top plugs have (3 / 8) inch threads to allow easy selective grasping for controlled insertion, rotation or withdrawal of each individual fuel tube.

7) The size of the minimum gap between adjacent 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 core rod fissionable matrerial concentration rapidly increases.

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

9) The spacing between adjacent fuel tubes is maintained by a (1 / 8) inch OD spiral stranded wire winding on every second fuel tube in a horizontal or vertical row. These windings are spot welded onto their respective fuel tubes. Each winding has about 2 turns / m. In this configuration each fuel bundle diagonal consists of either all unwound tubes or all spiral wound tubes. The spiral wound tube positions are chosen so that all the tubes adjacent to a diagonal reinforcing plate are unwound. Fuel tube spacing control is further enhanced by geometries of the shroud plates, diagonal plates and corner girders

10) In the channels between the fuel tubes liquid sodium coolant flows upwards to remove heat. Implications of this design are natural primary sodium 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.

11) The fuel tube wire winding thickness and pitch must ensure sufficient liquid sodium flow to a reactor hot spot to prevent formation of gaseous coolant bubbles (voids). If voids form the buoyancy force will be increased but the coolant mass flow might be reduced. We must check that there is no region of coolant thermal instability as the coolant flow cross section decreases or as the core fuel temperature increases.

12) A related issue is that the allowable maximum sodium temperature rise as liquid sodium passes through the fuel bundle is theoreticaly 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) and Pu-Fe fuel tube eutectic melting (602 degrees C) at the fuel tube inner surface.

13) In practise there are a number of temperature drops and other issues which must be taken into consideration which impose a lower limit on the primary liquid sodium coolant working temperature of about 340 degrees C and an upper limit on the high primary liquid sodium coolant working temperature of about 460 degrees C.

14) Based on these issues the fuel tube outside diameter (OD) was chosen to be:
0.500 inch
and the square lattice center to center spacing between adjacent fuel tubes was chosen to be:
(5 / 8) inch = 0.625 inch.

15) This dimension choice sets the normal smallest initial intertube gap in the assembly at:
(1 / 8) inch
which might reduce to:
(1 / 16) inch
after 12.5% linear fuel tube swelling, so filtering should be used to eliminate dirt particulates larger than (1 / 32) inch in longest dimension.

16) Each fuel tube position has associated with it a fuel bundle top surface area of about 1 tube per [0.625 inch]^2
= 1 tube / .3906 inch^2

17) The cross sectional area initially occupied by each unwound fuel tube is:
Pi (1 / 4)^2 inch^2 = 0.1963 inch^2

18)At the grating the cross sectional area per fuel tube is further reduced by:
4 X (1 / 16) inch X (1 / 8) inch = (1 / 32) inch^2
= 0.03125 inch^2

19) Thus the remaining initial cross sectional open area per active fuel tube available for natural convection liquid sodium coolant flow is:
0.3906 inch^2 - 0.1963 inch^2 - 0.03125 inch^2 = 0.1631 inch^2
= 0.1631 inch^2 X (.0254 m / inch)^2
= 1.0521 X 10^-4 m^2

20) Over the working life of a fuel tube its diameter in the core zone might swell from 0.500 inch to
1.125 X 0.5 inch:
. Hence in the core zone the fuel tube cross sectional area might swell to:
Pi [1.125]^2 [(0.25) inch]^2 = 0.2485 inch^2

21) Thus at that time the remaining cross sectional open area per core fuel tube in the core zone available for natural convection liquid sodium coolant flow is:
0.3906 inch^2 - 0.2485 inch^2 = 0.1421 inch^2
= 0.1421 inch^2 X (.0254 m / inch)^2
= 0.9168 X 10^-4 m^2

22) Hence the certain effective cross sectional area for sodium coolant circulation at the grating discharge is about:
0.9168 X 10^-4 m^2 / active fuel tube X 299,776 active fuel tubes = 27.483 m^2

23) The length of the reactor core zone perimeter is about:
Pi X 12.6 m = 39.58 m

24) Hence the vertical thickness of the radially horizontally moving liquid sodium layer at the reactor active region perimeter is about:
(27.483 m^2) / (39.58 m) = 0.694 m.
 

FUEL BUNDLE GRATING ENTRANCE:
The fuel tubes in a fuel bundle are held in position by the (1 / 8) inch thick sheet steel grating directly under the fuel tubes which is (1 / 4) inch thick on the bottom. The grating transfers the weight of the fuel tubes onto the adapter plates and then either the fuel bundle legs or a support pipe. It is of paramount importance that the adapter plate welds never structurally fail. Hence these welds must be tested at 3X their normal maximum load.

The grating strips need to be (1 / 8) inch thick on the top 3 x (5 / 8) inch and (1 / 4) inch thick on the bottom 2 X (5 / 8) inch. Then at the bottom of the grating the open area per fuel tube is:
(3 / 8) inch X (3 / 8) inch X (.0254 m / inch)^2 = 0.907 X 10^-4 m^2 / fuel tube.

The corresponding cross sectional area of primary sodium flow is:
299,776 active fuel tubes X 0.907 X 10^-4 m^2 / fuel tube
= 27.19 m^2

This is the smallest cross sectional area in the reactor primary sodium circulation loop.
 

SLOT APPROXIMATION:
For viscosity analysis purposes we can approximate the liquid sodium flow up past a fuel tube as a flow through a slot. Initially the length of the slot is half the perimeter length of the fuel tube or
Pi (1 / 2) inch (1 / 2) = 0.7854 inch
= 0.7854 inch X (.0254 m / inch) = 0.01995 m

Initially the open area is dominated by the grid open area, so the equivalent slot width is:
1.0521 X 10^-4 m^2 / 0.01995 m = 0.005274 m

After the fuel tube swells causing its diameter to increase by (1 / 16) inch the equivalent length of the slot becomes:
Pi (9 / 16) inch (1 / 2) = 0.8836 inch
= 0.8836 inch X 0.0254 m / inch = 0.02244 m

At this time the open area is core zone limited to:
9.168 X 10^-5 m^2
which gives an equivalent slot width of:
(9.168 X 10^-5 m^2) / (0.02244 m) = 0.004086 m
 

CORE ZONE FUEL SWELLING:
Practical operating experience with the EBR-2 reactor showed that during normal operation formation of fission products causes the core fuel 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.
 

CORE ZONE STEEL SWELLING
Due to the action of fast neutrons the fuel bundle material in the extended 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 bundles further apart to prevent this jamming, as that spacing will substantially reduce the average Pu-239 concentrations making attainment of core criticality difficult with old fuel.

In the extended core zone it is necessary to reduce the width of the fuel bundle diagonal reinforcing plates and to not weld these plates to the corner girders. The fuel bundles must be designed so that the extended core section of the fuel bundle can safely absorb the maximum torque associated with crane handling of the fuel bundles.

The present fuel bundle design provides at room temperature an ideal (3 / 4) inch clearance between the outer surface of the shroud plate of a movable fuel bundle and the outer surfce of the shroud plate of the adjacent fixed fuel bundles. With good dimensional tolerance control this clearance should be sufficient to allow reasonable core zone material swelling and thermal expansion. Note that in addition to fabrication tolerances this (3 / 4) inch space must absorb corner girder swelling and thermail expansion.
 

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 120 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 120 deg C X 13.125 inch = 0.039 inch
The fuel bundle leg sockets must accommodate this differential thermal expansion.
 

SWELLING AND THERMAL EXPANSION ALLOWANCE:
Over the working life of a fuel bundle the component linear dimensions in the reactor extended core region can potentially increase by as much as 12.5%. 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 movable 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.

The fuel bundles are designed so that individual fuel tubes, corner girders and diagonal plates can all linearly swell due to fast neutron bombardment in and adjacent to the core zone without the external width of the fuel bundle significantly changing. In the core zone the diagonal plates are reduced in width to provide a swelling allowance and the shroud plates are not welded to the corner girders.

Fuel bundles are intended to be replaced at 12.5% linear swelling of the most intensely neutron irradiated sections occurs. The fuel tube array center-to-center spacing is established by the support grid bottom geometry, by the spiral windings on every second fuel tube and by the corner girders, diagonal plates and shroud plates.

At the upper corners of the fixed fuel bundles are through bolts with spacers which are used to corner connect adjacent fixed fuel bundles and to prevent adjacent fixed fuel bundles sliding axially with respect to one another and hence prevent lateral rocking as might occur during a severe earthquake. At a corner spacer thickness of 0.707 inch the theoretical space between adjacent shroud plates is (3 / 4) inch.
 

CLEARANCE PENETRATIONS:
The extent of the movable fuel bundle corner girder penetration of the (3 / 4) inch clearance due to swelling is:
(1 / 8) X (10 / 8) inch X (1 / 2) = (10 / 128) inch

The extent of the fixed fuel bundle corner girder penetration of the (3 / 4) inch clearance due to swelling is:
(1 / 8) X (15 / 8) inch X (1 / 2) = (15 / 128) inch

The extent of the movable fuel bundle corner girder penetration of the (3 / 4) inch clearance due to thermal expansion is:
500 deg C X 20 / 10^6 deg C X 19 X (5 / 8) inch X (1 / 2) = 0.059375 inch

The extent of the fixed fuel bundle corner girder penetration of the (3 / 4) inch clearance due to thermal expansion is:
500 deg C X 20 / 10^6 deg C X 23 X (5 / 8) inch X (1 / 2) = 0.071875 inch

Thus the remaining clearance between the shroud plates available to accommodate fabrication tolerances is:
0.75 inch - (10 / 128) inch - (15 / 128) inch - 0.059375 inch - 0.071875 inch
= 0.75 inch - 0.1953 inch - 0.059375 inch - 0.071875 inch
= 0.4234 inch
 

FIXED FUEL BUNDLE DETAIL:
Each fixed fuel bundle is formed from double angle corner girders with side arms at 45 degrees to the base that displace 6 theoretical fuel tube positions at each corner. In addition there are 33 theoretical fuel tube positions displaced by reinforcing diagonal plates. Hence the actual number of fuel tubes contained in a fixed fuel bundle is:
21^2 - 4(6) - 33 = 384 fuel tubes

A fixed fuel bundle has corner girders which extend up past the fuel tubes and attach to the diagonal sheets that provide a central lifting point. On installation the corner girders of fixed fuel bundles connect to adjacent fixed fuel bundles by through bolts at the top of each corner girder and by sockets at the bottom of each corner girder lower leg extension to form a rigid matrix into which the smaller movable fuel bundles can be inserted. The sockets are firmly attached to the open steel support lattice. The sockets are tapered at their tops to allow practical blind mating with the fuel bundle legs with +/- 6 mm (+/- (1 / 4) inch) position error.

Once the fixed fuel bundles are installed their sockets keep the fixed fuel bundles faces parallel to the faces of the other fuel bundles.

The entire weight of the fixed fuel bundles is supported by lower corner girder extensions (legs). These legs extend ~ 1.5 m below the fuel tube bottoms to allow movable 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 reinforcing diagonal bracing.

The fixed fuel bundle shroud plates are:
[17 (5 / 8)] inch wide X (3 / 16) inch thick.
= 1.9922 in^2 in plan view cross sectional area

The bottom of each fixed fuel bundle leg is supported by half of an "E" socket that overlaps the fixed fuel bundle area allocation. With reference to the previous diagram the cross sectional area of each fixed fuel bundle double angle corner girder is:
[5 X (5/8) X (5 / 8)] inch^2
= 1.9531 inch^2

The fixed fuel bundle diagonal plates are:
(1 / 4) inch thick X [(2)^0.5 X (23 - 5)(5 / 8) inch] wide
= (1 / 4)inch thick X 15.9099 inch wide
= 3.9775 in^2 in cross sectional area
 

MOVABLE FUEL BUNDLE DETAIL:
In operation each movable fuel bundle's weight is borne by its hydraulic actuator which sets the amount of movable fuel bundle insertion into the matrix of fixed fuel bundles.

The movable fuel bundle travel is limited at its fully retracted position by the adapter plates and at its highest position by a hydraulic actuator vent hole.

There is a keyway to precisely rotationally orient a movable fuel bundle at its fully retracted position.

Each movable fuel bundle consists of diagonal reinforcing plates, corner girders and a shroud surrounding 248 vertical fuel tubes. A movable fuel bundle withdraws up to 1.0795 m relative to the fixed fuel bundle matrix to set the reactor operating temperature and to cause a reactor cool shutdown. The vertical position of each movable fuel bundle is set by its hydraulic actuator and is indicated by its Indicator Tube.

At the 4 corners of every movable fuel bundle are angle girders that displace 3 theoretical fuel tube positions at each corner. In addition there are 29 theoretical tube positions occupied by reinforcing diagonal plates. Hence the actual number of fuel tubes contained in a movable fuel bundle is:
17^2 - (4 X 3) - 29 = 248 fuel tubes

The movable fuel bundles have corner girders with sides that are each:
2 (5 / 8) inch = (10 / 8) inch long. The material is (5 / 8) inch thick. With reference to the previous diagram the cross sectional area of each such corner girder is:
3 X (5/ 8) inch X (5 /8) inch
= (75 / 64) inch^2
= 1.1719 inch^2

The movable fuel bundle diagonal reinforcing plates are (1 / 4) inch thick The width of each of these plates is:
(2)^0.5 X 15 X (5 / 8) inch = 13.2583 inch

The cross sectional area of each movable fuel bundle diagonal plate is:
(1 / 4) inch X 13.2583 inch = 3.3146 inch^2

The support pipe has a tapered bottom tip which aids blind insertion into the hydraulic cylinder. The piston has a tapered top projection with a maximum 6.81 inch OD which keeps the support pipe bottom centered on the hydraulic actuator piston. The support pipe piston has a piston ring with a 9.560 inch OD to match the 9.562 inch ID of the 10 inch schedule 80 pipe used as a hydraulic actuator cylinder.

One purpose of this arrangement is to hold the movable fuel bundle nearly vertical in the fully retracted position and properly oriented while its surrounding fixed fuel bundles are being installed. Once the fixed fuel bundles are in position the movable fuel bundle support pipe acts as a piston rod.

Each hydraulic actuator cylinder has a hole through its side near its top. The purpose of this hole is to release hydraulic pressure when the movable fuel bundle reaches its maximum insertion position. This hole also prevents 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 movable bundle should be installed in its fully withdrawn and straight upright and aligned position before installing its surrounding fixed fuel bundles. The rotational alignment in the fully withdrawn state is achieved via a keyway.

Similarly the fixed fuel bundles surrounding a movable bundle should be extracted from the fuel assembly before extracting the movable fuel bundle. That strategy ensures that the fuel assembly will not accidently go critical due to pulling a movable fuel bundle right through the matrix of fixed fuel bundles.

Thus the order of fuel bundle insertion and extraction is important. In assembly of the fuel bundle array a movable fuel bundle is ALWAYS installed fully retracted before its surrounding fixed fuel bundles are installed. Similarly, during disassembly of the fuel bundle array the fixed fuel bundles surrounding a movable fuel bundle are ALWAYS removed before removing the retracted movable fuel bundle.
 

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) Interlock the diagonal plates together like dividers in a wine box.
c) Weld the diagonal plates together along their lengths.
d) Weld the corner girders to the diagonal plates. Note that there is no welding near the core zone due to diagonal plate width reduction.
e) Insert the grating.
f) Weld the adapter plates to the support pipe if appropriate.
g) Weld the tapered centering devices to the support pipe.
[1.00 inch wide X (9.562 inch - 8.625 inch) / 2 inch]
= 1.00 inch wide X 0.4685 inch thick
at top.
h) Weld the adapter plates to the corner girders.
i) Check the mechanical strength of the adapter plate support of the grating.
j) Weld on the shroud sheets with just external welds.
k) Attach the filter housings and filters as applicable.
l) Check the entire fuel bundle basket for dimensional compliance.
m) Insert the fuel tubes.
n) Apply a temporary fuel tube retainer plate.
 

FUEL BUNDLE CRANE LIFTING:
The fuel bundles are designed to be sufficiently robust to permit reasonable crane handling. 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 bending torque resistance requirement implies a transverse acceleration resistance of 0.5 g when the fuel bundles are bottom supported. This bending torque resistanc requirement sets minimums on the thickness of the fuel bundle shroud plates, diagonal plates, corner girders, support pipe and leg bracing.

The lifting point for a fuel bundle is a group of four holes in 0.25 inch thick diagonal plates. These diagonal plates and the corresponding corner girders and shroud plates extend:
13 X (5 / 8) inch = 8.125 inch
above the maximum height of the fuel tube top plugs.

Four 2 inch diameter holes in these plates form a lifting point with a maximum lifting capacity of:
4 X 2 inch X (1 / 4) inch X 10,000 lbs / inch^2 = 20,000 lbs = 10 tons.

Note that the crane lifting device is a special four pin device that provides one snugly fitting pin for each hole in the diagonal plates. The four pins have expanded ends which engage four holes located near the top of the diagonal sheets.

The diagonal plates forming the lifting point must not obstruct primary liquid sodium flow and must not prevent individual fuel tube insertion or extraction. The fuel tube top plugs have (3 / 8) inch threads and the OD of the fuel tube insertion / removal tool cannot be more than (5 / 8) inch.

The corner girders of the fixed fuel bundles must project upwards above the top of the diagonal plates by about:
6 (5 / 8) inch = 3.75 inch
to allow for a 3.5 inch long 0.5 inch diameter horizontal bolt fastening to adjacent fixed fuel bundles at the top of the corner girders.

The bottom of the fuel bundle lifting point holes must be at least 2 inch above the top of the fuel tube top plugs.
 

INDICATOR TUBE:
There are 7.5 m high buoyant indicator tubes field attached to the movable active fuel bundles. The vertical position of each movable 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 movable square fuel bundle, allows measurement of the gamma flux emitted vertically by the movable fuel bundle and allows determination of that movable fuel bundle's steady state discharge temperature.

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

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

Indicator tubes are attached to the movable fuel bundles after the movable fuel bundles are installed and are removed before the movable fuel bundles are relocated. The indicator tube attachment point is the movable fuel bundle lifting point. 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 movable fuel bundle liquid sodium discharge temperature measurement. The difference between the indicator tube OD and ID provides a hollow path for gamma radiation to reach the overhead FNR monitoring apparatus.

An indicator tube isolates a movable 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 movable 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 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 positions and horizontally stabilizes the hydraulic cylinders. This open 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 8 inch schedule 160 support pipe maintains separation between the bottom of the movable fuel tubes and the hydraulic actuator piston. This separation extends the working life of the hydraulic actuators. The fixed fuel bundle legs keep the bottom of the fixed fuel bundle tubes about 1.5 m above the open steel lattice to protect the open steel lattice from neutron damage. The sockets mounted on the top of the open steel lattice correctly position the fixed fuel bundles. Blind insertion is assisted by the upright position of the four adjacent retracted movable fuel bundles. A fixed fuel bundle can be released from its socket by removing its 4 top corner "E" fitting bolts and then lifting the fixed fuel bundle using the overhead gantry crane.
 

BENDING TORQUE RESISTANCE CONSIDERATIONS:
A major issue in fuel bundle design is its bending torque resistance because the overall fuel bundle height of 8.001 m is much greater than its width (.2794 m for movable fuel bundles or 0.3429 m for fixed fuel bundles). Hence, the mechanical design of the fuel bundles is important to ensure that during fabrication, transport, installation and operation the fuel bundles do not deform. Such deformation could potentially cause a jam in the sliding of a movable fuel bundle within the surrounding matrix of fixed fuel bundles.

A fixed fuel bundle has corner girders which extend up past the fuel tubes. These girders top attach to adjacent fixed fuel bundles by through bolts at the top of each corner girder and by sockets at the bottom of each corner girder lower leg extension. The sockets are firmly attached to the open steel support lattice. The sockets are tapered at their tops to allow practical blind mating with the fuel bundle legs with +/- 6 mm (+/- (1 / 4) inch) position error.
 

The entire weight of the fixed fuel bundles is supported by lower corner girder extensions (legs). These legs extend ~ 1.5 m below the fuel tube bottoms to allow movable 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 reinforcing diagonal members.

In operation each movable fuel bundle's weight is borne by its hydraulic actuator which sets the amount of movable fuel bundle insertion into the matrix of fixed fuel bundles. The movable fuel bundle travel is limited at the bottom by the unreinforced support pipe length (1.1 m) and at the top by a hydraulic actuator vent hole.

The fuel tube spacing within a fuel bundle is maintained using a spiral (1 / 8) inch diameter stranded wire winding spot welded onto every second fuel tube and by the diagonal and shroud plates.
 

REACTOR TEMPERATURE SETPOINT CONTROL:
In normal reactor operation the movable fuel bundles insert into the matrix of fixed fuel bundles from the below. When all the movable fuel bundles are fully inserted into the fixed fuel bundle matrix the reactor is at maximum reactivity. When all the movable 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 movable fuel bundle and its surrounding active fixed fuel bundles can almost be regarded as an independent FNR. Each movable fuel bundle has its own discharge temperature which is set by the amount of insertion of the movable fuel bundle into the fixed fuel bundle matrix. Under cold shutdown conditions gravity causes all the movable fuel bundles to withdraw 1.2 m with respect to the fixed fuel bundle matrix.

When the movable active fuel bundles are fully inserted into the fixed fuel bundle matrix there is a ~ 1.5 m high nearly open space outside the support pipes that allows almost unimpeded liquid sodium circulation.
 

BLOCKED COOLANT FLOW CHANNELS:
Between every set of four adjacent fuel tubes is a coolant flow channel. If one isolated coolant flow channel becomes blocked by a distorted fuel tube, dirt or debris the cooling of each of these four adjacent fuel tubes is reduced by 25% and the temperture rise along these fuel tubes potentially increases by 33%. If two adjacent coolant flow channels are blocked the flow of coolant for the most affected fuel tubes is reduced by 50% and the temperature rise along these fuel tubes potentially increases by 100%. Hence, fuel bundles should be designed so that the fuel bundle can safely accommodate a 100% increase over normal in the cooling fluid temperature rise along the fuel tube.

There are really two constraints, one is the safe maximum coolant temperature and the other the the safe maximum fuel temperature. Of these two, normally the maximum fuel temperature is the more confining upper limit. If the maximum allowable temperature rise is:
100 degrees C,
normal coolant temperature rise along the fuel tube must be less than:
(1 / 2) X 100 deg C = 50 degrees C
which implies a worst case sodium operating temperature range from 410 deg C to:BR> 410 deg C + 100 deg C = 510 C deg C
and a worst case fuel centerline operating temperature range of:
460 deg C + 100 deg C = 560 deg C.
 

FUEL BUNDLE INLET FILTERS:
At the bottom of each fuel bundle are potentially 4 filter sections beetween and supported by the adapter plates. The purpose of these filters is to prevent particulate matter suspended in the primary liquid sodium from blocking the cooling flow channels between adjacent fuel tubes. These filters should 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.

Downstream from the filter material is a void space that allows redistribution of primary sodium flow in the event that one of the filter sections is obstructed. Every practical means should be used to keep particulate material out of the primary sodium pool. The lower portion of the primary sodium pool should be kept above 320 degrees C to prevent NaOH precipitation on intermediate heat exchange surfaces and on the filters. Operating at 410 degrees C avoids the melting points of KOH, MgOH, Al(OH)3, etc. In the event that a filter is partially plugged the liquid sodium circulation through that filter will decrease causing the fuel bundle's discharge temperature to increase and the gamma/neutron output to fall, indicating a problem with a flow obstruction of that fuel bundle.

Note that any potassium in the primary liquid sodium will tend to precipitate out at about 360 deg C, so potasium is a potential steam generator 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.
 

CORNER GIRDER CROSS SECTION:
Each fixed fuel bundle is structurally stabilized by its rigid outer corner double angle girders, shroud plates and diagonal plates. The cross sectional area of each of these fixed fuel bundle corner girders is:
= 5 X (5 / 8) inch X (5 / 8) inch = 1.9531 inch^2

Each movable fuel bundle is structurally stabilized by its rigid corner girders, shroud plates and diagonal plates. The cross sectional area of each movable fuel bundle corner girder is:
3 X (5 / 8) inch X (5 / 8) inch = 1.1719 inch^2.
 

FIXED FUEL BUNDLE MASS:
Each fixed fuel bundle is structurally stabilized by its rigid outer corner double angle girders, shroud plates and diagonal plates. The cross sectional area of each of these fixed fuel bundle corner girders is:
= 5 X (5 / 8) inch X (5 / 8) inch = 1.9531 inch^2

Forming the outer shroud on each fixed fuel bundle are 4 X (3 / 16) inch thick steel plates, each 10.625 inches X 268.75 inch. The volume of these shroud plates is:
4 X 10.625 inch X 268.75 inch X (3 / 16) inch X (.0254 m / inch)^3 = 0.03509456 m^3

The mass of the fixed fuel bundle shroud plates is:
+ (0.03509456 m^3) X 7.870 X 1000 kg / m^3
= 276.194 kg

The mass of the four fixed fuel bundle corner girders is:
4 X 1.9531 inch^2 X 8.001 m X (0.0254 m / inch)^2 X 7.870 X 10^3 kg / m^3
= 317.34 kg

The fixed bundles have two diagonal reinforcing plates, each:
2^0.5 X 18 X (5 / 8) inch = 15.91 inches wide. The mass of the diagonal sheets is:
2 X 15.91 inch X 1 / 4 inch X 404 X (5 / 8) inch X (0.0254 m / inch)^3 X 7.870 X 10^3 kg / m^3
= 259.046 kg.

The bottom steel grating of a fixed fuel bundle is composed of 42 pieces of .125 inch X 5 X (5 / 8) inch X 13.125 inch steel, for a total volume of:
42 pieces / bundle X .125 inch X (25 / 8) inch X 13.125 inch = 215.33 inch^3

The mass of each fixed fuel bundle's bottom grating is:
215.33 inch^3 X (0.0254 m / inch)^3 X 7.870 X 1000 kg / m^3 = 27.77 kg

The mass of each fixed fuel bundle's adapter plates is:
2 X 1.00 inch X 26 X (5 / 8) inch X 15.91 inch X (.0254 m / inch)^3 X 7870 kg / m^3 = 66.685 kg

The mass of each fixed fuel bundle's leg bracing is: ______

From FNR Fuel Tubes each active fuel tube has a mass of 6.884 kg

Each fixed octagonal fuel bundle contains 384 fuel tubes, each with a mass of 6.884 kg. Hence the mass of fuel tubes is:
384 tubes X 6.884 kg / fuel tube = 2643.5 kg

TOTAL FIXED FUEL BUNDLE MASS:
384 loaded fuel tubes + 4 shroud plates + 4 fixed fuel bundle corner girders + 2 diagonal plates + octagonal bundle grating + adapter plates + bracing
2643.5 kg + 276.194 kg + 317.34 kg + 259.046 kg + 27.77 kg + 66.685 kg +___
= 3590.535 kg + _____
~ 3.7 tonnes

Missing from this calculation is the mass of the bottom diagonal cross bracing.

Note that each fixed fuel bundle grating section must transfer the weight of 384 loaded fuel tubes onto the adapter plates and then onto the outer corner girders which support the fuel bundle. Immediately below each grating section are the four entrance filter sections.
 

FIX FROM HERE - GRATING LOAD IS OF CONCERN

MOVABLE FUEL BUNDLE:
Each movable fuel bundle is structurally stabilized by its rigid corner girders, shroud plates and diagonal plates. The cross sectional area of each movable fuel bundle corner girder is:
3 X (5 / 8) inch X (5 / 8) inch = 1.1719 inch^2.
 

The shroud plates of a movable fuel bundle weigh:
4 X [15 (5 / 8)] inches X (3 / 16) inch X 428 X (5 / 8) inch X (.0254 m / inch)^3 X 7.870 X 10^3 kg /m^2
= 224.91 kg / shroud.

Each movable fuel bundle has four corner girders weighing:
4 X (1.1719) inch^2 X 6.3 m X (.0254 m / inch)^2 X 7.870 X 10^3 kg / m^3
= 149.942 kg

The movable fuel bundles each have two diagonal reinforcing plates weighing:
2 X [13.258] inches X (1 / 4) inch X 6.3 m X (.0254 m / inch)^2 X 7.870 X 10^3 kg /m^3
= 212.05 kg
 

The bottom steel grating of a movable fuel bundle is composed of 34 pieces of 0.125 inch X 4.0 inch X 10.625 inch steel, for a total volume of:
34 pieces / bundle X .125 inch X 4.0 inch X 10.625 inch = 180.625 inch^3

The mass of each movable fuel bundle's bottom grating is:
180.625 inch^3 X (0.0254 m / inch)^3 X 7.870 X 1000 kg / m^3 = 23.29 kg

A movable fuel bundle has a 8 inch schedule 160 bottom support pipe 1.555 m high, 8.625 inch OD, 6.813 inch ID weighing:
{Pi [(8.625 inch)^2 - (6.813 inch)^2] / 4} X 1.555 m X (.0254 m / inch)^2 X 7.870 X 10^3 kg / m^3
= {Pi [74.3906 inch^2 - 46.417 inch^2] / 4} X 1.555 m X (.0254 m / inch)^2 X 7.870 X 10^3 kg / m^3
= 145.02 kg

The mass or each movable fuel bundle's adapter plates is:
_______

From FNR Fuel Tubes each active fuel tube has a mass of 6.884 kg.

A movable fuel bundle has 248 fuel tubes each weighing 6.884 kg for a total fuel tube weight of:
248 fuel tubes X 6.884 kg / fuel tube = 1707.2 kg.

Thus the total weight of a movable fuel bundle is:
248 loaded fuel tubes + 4 shroud plates + 4 corner girders + 2 diagonal plates + octagonal bundle grating + support pipe
1707.2 kg + 224.91 kg + 149.942 kg + 212.05 + 23.29 kg + 145.02 kg= 2462.01 kg

The movable fuel bundle bottom grating must transfer the weight of 248 loaded fuel tubes onto the fuel bundle's diagonal plates, shroud and outer corner girders and then to the support pipe while still permitting unobstructed primary liquid sodium flow. The support pipe must allow unobstructed primary liquid sodium flow while bearing the load imposed by the movable fuel bundle.

The above calculation does not include the weight of the adapter plates or the centering devices or the support pipe bottom taper.
 

TOTAL FIXED FUEL BUNDLE + MOVABLE FUEL BUNDLE CROSS SECTIONAL AREA ALLOCATION:
The total core zone cross sectional area allocation for this pair of fuel bundles is:
(area of movable fuel bundle) + (area of fixed fuel bundle)
= (19 X 5 / 8)^2 inch^2 + (23 x 5 / 8)^2 inch^2 - 8 (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
 

FUEL BUNDLE CORE ZONE STEEL CROSS SECTIONAL AREA:
Each fixed fuel bundle is structurally stabilized by its rigid outer corner double angle girders, shroud plates and diagonal plates. The cross sectional area of each of these fixed fuel bundle corner girders is:
= 5 X (5 / 8) inch X (5 / 8) inch = 1.9531 inch^2

Each movable fuel bundle is structurally stabilized by its rigid corner girders, shroud plates and diagonal plates. The cross sectional area of each movable fuel bundle corner girder is:
3 X (5 / 8) inch X (5 / 8) inch = 1.1719 inch^2.

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:
(384 + 248) tubes X Pi (0.25^2 - (0.25 -0.035)^2) inch^2 / tube
= (632) tubes X Pi (0.0625 - 0.046225) inch^2 / tube
= 32.314 inch^2

Fixed fuel bundle shroud sheets:
4 X (3 / 16) inch X [18 X (5 / 8)] inch = 8.4375 inch^2

Fixed fuel bundle corner girders:
4 X 5 (5 / 8 inch)^2 = 7.8125 inch^2

Fixed fuel bundle diagonal plates: 2 X (1 / 4) inch X 2^0.5 X 18 X (5 / 8) inch = 7.955 inch^2

Movable fuel bundle shroud sheets:
4 X (3 / 16) inch X 15 X (5 / 8) inch = 7.031 inch^2

Movable fuel bundle corner girders:
4 X 3 X (5 / 8 inch)^2 = 4.6875 inch^2
 

Movable fuel bundle diagonal plates:
2 X (1 / 4) inch X 2^0.5 X 15 X (5 / 8) inch = 6.6291 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:
32.314 inch^2 + (8.4375 inch^2 + 7.8125 inch^2 + 7.955 inch^2)
+ (7.031 inch^2 + 4.6875 inch^2 + 6.6291 inch^2)
= 75.0108 inch^2
= 74.8667 inch^2 X (.0254 m / inch)^2
= 0.048301 m^2
 

STEEL CROSS SECTIONAL AREA FRACTION:
Hence in the core zone the fractional cross sectional area occupied by steel is:
74.8667 inch^2 / 344.53 inch^2
= 0.21730
 

CORE FUEL ROD CROSS SECTIONAL AREA FRACTION:
Calculate over one fixed fuel bundle + one mobile fuel bundle:
(384 + 248) 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:
0.040206 m^2 / 0.2222777 m^2
= 0.180882
 

SODIUM CROSS SECTIONAL AREA FRACTION:
= 1.0 - steel cross sectional area fraction - fuel rod cross sectional area fraction
= 1.0 - 0.21730 - 0.180882
= 0.60101
 

SUMMARY OF INITIAL CORE ZONE CROSS SECTIONAL AREA FRACTIONS:
Sodium = 0.60101
Core Fuel = 0.180882
Steel = 0.21730
 

MINIMUM REQUIRED BENDING TORQUE RESISTANCE FOR CRANE MANIPULATION OF FIXED FUEL BUNDLES:
To allow crane manipulation of individual fixed fuel bundles the fixed fuel bundle transverse torque resistance must be at least:
(3605 kg / 2) X (8.0 m / 2) X 9.8 m / s^2 = 70,658 N-m
= 70,658 N-m X (1 inch / 0.0254 m) X 1 lb / (.454 kg X 9.8 m / s^2)
= 625,238 inch-lbs
which permits one end of a single fixed fuel bundle to be picked up by a crane.
 

FIXED BUNDLE SIDE SHEET BENDING 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 for a fixed fuel bundle:
W = 0.1875 inch;
L = 17 X (5 / 8) inch = 10.625 inch;
Sy = 30,0000 lb / inch^2;
giving:
Tor = W L^2 Sy / 18
= 0.1875 inch (10.625 inch)^2 X (30,000 lb / 18) inch^2
= 35,278 inch-lbs.

Hence the torque resistance due to the two shroud side plates is:
2 X 35,278 inch-lbs = 70,556 inch-lbs.
 

FIXED FUEL BUNDLE SHROUD TOP AND BOTTOM SHEET BENDING TORQUE RESISTANCE:
2 X 10,000 lb / inch^2 X (3 / 16) inch X 10.625 inch X 10.5 inch
= 418,359 inch-lbs.
 

FIXED FUEL BUNDLE CORNER GIRDER BENDING TORQUE RESISTANCE:
4 X 10,000 lb / inch^2 X 5 X [(5 / 8) in]^2 X 9.5 inch
= 742,187 inch-lbs
 

FIXED FUEL BUNDLE DIAGONAL PLATE BENDING TORQUE RESISTANCE:
One diagonal plate will provide 2^0.5 X the working torque resistance as one side sheet of the same thickness or:
(2^0.5)(35,278 inch-lbs) = 49,871 inch-lbs.
Hence two diagonal plates provide:
2 X 49,871 = 99,781 inch-lbs.
 

TOTAL FIXED FUEL BUNDLE BENDING TORQUE RESISTANCE:
Hence the total bending torque resistance for the fixed fuel bundles is:
70,556 inch-lbs + 418,359 inch-lbs + 742,187 inch-lbs + 99,781 inch-lbs
= 1,330,883 inch lbs
 

REQUIRED BENDING TORQUE RESISTANCE FOR CRANE MANIPULATION OF MOVABLE FUEL BUNDLES:
To allow crane manipulation of individual movable fuel bundles the movable fuel bundle transverse torque resistance must be at least:
(2365 kg / 2) X (8.0 m / 2) X 9.8 m / s^2 = 46,354 N-m
= 46,354 N-m X (1 inch / 0.0254 m) X 1 lb / (.454 kg X 9.8 m / s^2)
= 410,177 inch-lbs
which permits one end of a single fixed fuel bundle to be picked up by a crane.
 

MOVABLE FUEL BUNDLE SIDE PLATE BENDING TORQUE RESISTANCE:
From the plan view diagram:
W = 0.1875 inch;
L = 15 (5 / 8) inch = 10.625 inch;
Sy = 30,0000 lb / inch^2;
giving:
Tor = W L^2 Sy / 18
= 0.1875 inch (9.375)^2 inch^2 X 30,000 lb / 18 inch^2
= 27,466 inch-lbs.

Hence the two side plates provide:
2 X 27,466 = 54,932 inch lbs of torque resistance.
 

MOVABLE FUEL BUNDLE SHROUD TOP AND BOTTOM SHEET BENDING TORQUE RESISTANCE:
2 X 10,000 lb / inch^2 X (3 / 16) inch X 15 (5 / 8) inch X 17 (5 / 8)(1 / 2) inch
= 186,768 inch-lbs.
 

MOVABLE FUEL BUNDLE SHROUD CORNER GIRDERS BENDING TORQUE RESISTANCE:
4 X 10,000 lb / inch^2 X 3 X [(5 / 8) inch]^2 X 15 (5 / 8 inch) (1 / 2)
= 219,726 inch-lbs
 

MOVABLE FUEL BUNDLE DIAGONAL PLATE BENDING TORQUE RESISTANCE:
Each of two diagonal platses will 2^0.5 X the working torque resistance as the two side plates of the same thickness or:
(2^0.5) (54,932 inch-lbs) = 77,686 inch-lbs.
 

MOVABLE FUEL BUNDLE TOTAL BENDING TORQUE RESISTANCE:
Hence the total transverse working torque resistance for a movable fuel bundle is:
54,932 inch lbs + 186,768 inch-lbs + 219,726 inch-lbs + 77,686 inch-lbs
= 539,112 inch lbs

Hence the main body torque resistance is sufficient for crane manipulation.
 

MOVABLE FUEL BUNDLE SUPPORT PIPE:
Use a 1.5 m length of 8 inch schedule 160 steel pipe. OD = 8.625 inch
Wall thckness = 0.906 inch
ID = 6.813 inch

Bending Torque Resistance = 2 X Integral from Theta = 0 to Theta = Pi of Integral from R = Ra to R = Rb of:
dR R dTheta R sin(Theta) (Sy / 3)
= 2 X Integral from Theta = 0 to Theta = Pi of:
[(Rb^3 - Ra^3) / 3](Sy / 3) sin(Theta) d(Theta)
= 2 [(Rb^3 - Ra^3) / 3](Sy / 3)[- cos(Pi) - (- cos(0))]
= 2 [[(Db / 2)^3 - (Da / 2)^3] / 3] (Sy / 3)[1 + 1]
= (1 / 6)[Db^3 - Da^3] (Sy / 3)
= (1 / 6)[(8.625 inch)^3 - (6.813 inch)^3][10,000 lb / inch^2]
= (1 / 6)[641.619 - 316.238]inch^3 [10,000 lb / inch^2]
= 542,302 inch lbs
which is sufficient.
 

MOVABLE FUEL BUNDLE ADAPTER PLATE BENDING TORQUE RESISTANCE:
At any instant in time the equivalent of two adapter plates are conveying torque. Let L be the vertical length of one adapter plate. The torque that it conveys is:
2 X Integral from Z = 0 to Z = L / 2 of:
[Z / (L / 2)] [10,000 lb / in^2] W dZ Z
= 2 [2 Z^3 / 3 L][10,000 lb / in^2] W |Z = (L / 2)
= 4 [(L / 2)^3 / 3 L][10,000 lb / in^2] W
= 4 [L^2 / 24][10,000 lb / in^2] W
= [L^2 / 6][10,000 lb / in^2] W

Assume that adapter plate thickness is:
W = 1.000 inch

The required bending torque resistance by each movable fuel bundle adapter plate is:
[542,302 inch lbs / 2] = [L^2 / 6][10,000 lb / in^2] W
or
[542,302 inch lbs] = [L^2 / 3][10,000 lb / in]
or
L^2 = [3 X 542,302 inch lbs] / [10,000 lb / in]
= [3 X 54.2302 inch^2]
= 162.69 inch^2
or
L = 12.755 inch

This figure is significant because it means that we nust allow 0.4 m of height for the adapter plate including its top overlap of the support pipe and its bottom overlap of the movable fuel bundle corner girder.

HYDRAULIC ACTUATOR:
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 schedule 80 steel pipe (9.562 inch ID) with an internal piston. The movable fuel bundle has a 1.555 m long X 8.625 inch OD support pipe from the adapter plates to the piston. This support pipe holds the movable fuel bundle vertical when the support pipe is fully retracted. The support pipe OD (8.625 inches) is less than the hydraulic cylinder ID (9.562 inch). The support pipe has a bottom taper for smooth blind insertion into the hydraulic cylinder. The piston has a vertical top cone to center the support pipe on the piston.

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

The extent of insertion of a movable 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 position feedback from the associated indicator tube which indicates the movable fuel bundle vertical position. The hydraulic fluid feed tube is routed through the open steel lattice. This hydraulic tube must be sufficiently flexible to allow for +/- 1.0 m earthquake induced movement of the fuel assembly with respect to the walls of the primary sodium pool.

In the event of a hydraulic cylinder jam a section of open steel lattice containing hydraulic cylinder may have to be removed and replaced.

To cause a movable 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:
Pi (9.562 inch / 2)^2 X 100 lb / inch^2 = 7181 lb
of lifting force to raise the movable fuel bundle. If the piston attempts to move too high the high pressure liquid sodium underneath 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 movable 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 movable fuel bundle hydraulic drain valve used for reactor safety shutdown is not orifice restricted.
 

HYDRAULIC ACTUATOR COMPONENTS:
There is a 0.12 m high X 9.56 inch OD piston that slides within the 10.75 inch OD X 9.562 inch ID X 1.5 m high hydraulic cylinder made from 10 inch schedule 80 steel pipe to cause insertion of a movable fuel bundle into the matrix of fixed fuel bundles.
 

HYDRAULIC CYLINDER:
Fabricated from 10 inch schedule 80 steel pipe. OD = 10.750 inch
ID = 9.562 inch
Wall = 0.594 inch

Bending Torque resistance is:
Tor = (1 / 6) (Db^3 - Da^3) (Sy / 3)
= (1 / 6)[(10.750 inch)^3 - (9.562 inch^3)](10,000 lb / inch^2)
= (1 / 6)[1242.2969 inch^3 - 874.2713 inch^3](10,000 lb / inch^2)
= 613,376 inch-lb

Mass = Pi (10.750^2 - 9.562^2) inch^2 / 4 X 1.555 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3
= Pi (115.5625 - 91.432) inch^2 / 4 X 1.555 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3
= 144.42 kg

______

Hydraulic cylinder (1 / 2) inch thick bottom disk:
Mass = Pi (9.562 inch / 2)^2 X 0.5 inch X (.0254 m / inch)^3 X 7.874 X 10^3 kg / m^3
= 4.633 kg

Hydraulic Cylinder Piston:
Piston Mass = Pi (9.562 inch / 2)^2 X 4 inch_____ X (.0254 m / inch)^3 X 7.874 X 10^3 kg / m^3
= 37.06 kg

Hydraulic Cylinder Piston Centering Cone: ___________

FUEL BUNDLE TRANSPORT:
The fixed fuel bundle dimensions 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 with the fuel tube bottom forward to ensure that the fuel tubes, fuel rods and sodium all remain near the bottom of the fuel bundle.

The shipping 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.
 

QUANTITIES OF FUEL BUNDLES:
A practical 300 MWe modular Fast Neutron Reactor (FNR) contains 1149 active and passive fuel bundles and has additional mounting space for up tp 220 cooling fuel bundles.
 

This web page last updated September 29, 2021

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