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

Indicator tubes are 6.8 m high buoyant vertical, coaxial thin wall steel tubes that project 0.2 m to 1.3 m above the surface of the primary liquid sodium pool. The outer tube is 8.625 inch OD, 0.148 inch wall (Schedule 10). The inner tube is 1.315 inch OD, 0.109 inch wall (Schedule 10). The annular space between the two tubes is argon filled. A standard FNR has 464 indicator tubes visible above the core zone of the reactor. In addition there are about 4700 buoyant 9 inch diameter stainless steel spheres floating on the primary liquid sodium.

The purpose of the indicator tubes is to indicate to the overhead FNR monitoring system:
a) The insertion depth of each movable fuel bundle into the matrix of fixed fuel bundles;
b) The gamma flux originating from each movable fuel bundle;
c) The liquid sodium discharge temperature of each movable fuel bundle.

Note that the floating sphere OD is selected to be similar to the Indicator Tube OD so that on average over the reactor core zone there are three floating spheres for each indicator tube to provide good surface coverage of the primary liquid sodium.

There are positively buoyant indicator tubes attached to the movable fuel bundles. These indicator tubes extend vertically 0.2 m to 1.3 m above the primary liquid sodium coolant surface. The indicator tubes are field attached to the lifting points on the movable fuel bundles.

Each indicator tube consists of a central 1.315 inch OD with 0.109 inch wall steel tube open at the bottom with a flat top hat containing a pin hole and a surrounding thermally isolating concentric sealed buoyant argon gas filled annular region defined by a 8.625 inch OD, 0.148 inch wall steel tube. The annular region thermally isolates the central region ensuring that the temperature of the liquid sodium in the central tube is approximately the same temperature as the liquid sodium discharge temperature of the associated movable fuel bundle.

The outside steel tube, which is thermally isolated from the inside steel tube, must withstand the external primary liquid sodium head pressure and the internal argon gas pressure. The bottom metal spacer and the top thermally insulating spacer between the inner and outer tubes keeps the annular region gas sealed.

The annular argon gas filled region, in combination with the movaable fuel bundle fuel tube plenum regions, provides a low density path for gamma rays to pass through the primary liquid sodium bath. The gammma ray flux indicates the relative fission power of each movable fuel bundle.

The central tube top cover has a small hole to vent gases trapped in the central tube. This top cover is made of a material that has a high near infrared radiation emissivity.

The annular region of the indicator tube provides sufficient positive buoyancy so that when 1.3 m of the indicator tube is projecting above the primary liquid sodium surface the indicator tube maintains an upright position due to its positive buoyancy in hot liquid sodium.

Note that the buoyancy of the annular region is not sufficient to lift the net weight of a movable fuel bundle when the indictor tube is fully immersed in liquid sodium.

The inner tube of each indicator tube assembly extends slightly above the outer tube. At the top each central tube is a 8.625 inch diameter flat thermally conductive top cover which is thermally bonded to the inner steel tube. This top cover has a small central hole that keeps the top pocket gas pressure inside the inner tube equal to the outside ambient gas pressure.

The bottom of this top cover is thermally insulated. Its flat upper surface emits infrared radiation which indicates its temperature and hence the temperature of the movable fuel bundle liquid sodium discharge. The precision and reproducibility of this temperature indication is an important aspect of FNR temperature monitoring.

In operation,the liquid sodium level in the indicator tube central tube is approximately the same as the liquid sodium level outside the indicator tube.

Each indicator tube presents a 8.625 inch diameter round elevation target to an overhead laser scanner. If the distance from the laser to the apparent target position is too long it means that the laser is not looking at a valid target.

Note that when the movable fuel bundles are fully inserted into the matrix of fixed fuel bundles the indicator tube top covers are about 1.3 m above the primary liquid sodium coolant surface.

This top cover emits IR radiation indicating its temperature.

Gamma radiation passes up inside the fuel tube plenums, through the fuel tube top plugs, through the liquid sodium near the indicator tube attachment point, through the Indicator Tube bottom annular spacer, up the annular gas space inside the indicator tube, through the top annular thermal insulator and then through the indicator tube top hat. Note that the top annular insulator is normally out of the liquid sodium so its argon gas seal is not challenged by continuous direct exposure to hot liquid sodium. Note that the bottom annular spacer can be metal because at the bottom of the indicator tube the internal sodium and the external sodium are at the same temperature.

There are 6.8 m high buoyant indicator tubes field attached to the lifting points of movable active fuel bundles. The vertical position of each active movable fuel bundle is visually indicated by the 0.2 m to 1.3 m exposed height of the top of its indicator tube above the primary liquid sodium surface.

Indicator tubes are attached to the movable fuel bundle lifting points after the movable fuel bundles are installed and are removed before the movable fuel bundles are repositioned. The indicator tube attachment points are the movable fuel bundle lifting points. Each indicator tube has a dual J type bottom hook for attachment to the lifting points of a movable fuel bundle.

A FNR fuel bundle lifting point is achieved by replacing the (3 / 16) inch thick diagonal plates with (3 / 8) inch thick diagonal plates in the upper portion of the fuel bundle where there are mo fuel tubes. Two 3.0 inch diameter holes in each diagonal plate form the lifting points.

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 tube diameter should be minimal to minimize obstruction of the natural liquid sodium circulation, but must be sufficient to allow accurate steady state movable fuel bundle liquid sodium discharge temperature measurement.

The indicator tubes are fabricated from HT-9 steel (85% Fe, 12% Cr, 1% Mo, 0% C, 0% Ni). When the movable fuel bundle is fully inserted the length of the indicator tube plus hook places the top of the indicator tube 7.4 m above the top of the movable fuel tubes. Hence the indicator tube itself is only about:
6.0 m - 0.5 m + 1.3 m = 6.8 m long.

The height allowances for the fixed fuel bundle components from bottom to top are: legs including bottom grating (1.5 m), fuel tubes including end plugs (6 m), top of fuel bundle (0.4 m), swelling allowance 0.1 m. Hence the fuel bundle shipping container and the air lock tube must be able to accommodate a fuel bundle with an overall fuel bundle length of 8.0 m.

This same air lock is long enough to accommodate indicator tubes.

Indicator Tube:
[(8.625 inch OD X 0.148 inch wall) + (1.315 inch OD X 0.109 wall)] X 6.8 m long

Indicator Tube Mass:
Mass = Pi X [(8.625 inch X 0.148 inch) + (1.315 inch X 0.109 inch] X 6.8 m X 7.874 g / cm^3
= Pi [1.2765 inch^2 + 0.14335 inch^2] X 6.8 m X 7.874 X 10^3 kg / m^3
= Pi [1.41985 inch^2] X 6.8 m X 7.874 X 10^3 kg / m^3

Displaced Volume = Pi[(4.3125 inch)^2 - (.5485 inch)^2] X 6.8 m
= Pi [18.59766 inch^2 - 0.30085 inch^2] X 6.8 m
= Pi [18.2968 inch^2] X 6.8 m

Average density = Mass / displaced volume
=[1.41985 inch^2] X 7.874 X 10^3 km /m^3 / 18.2968 inch^2
= 0.61103 X10^3 kg / m^3

When 1.3 m of the tube is projecting above the liquid sodium surface the mass stays the same but the displaced length decreases to:
6.8 m - 1.3 m = 5.5 m.
In effect the average density increases to:
0.61103 X 10^3 kg / m^3 X 6.8 m / 5.5 m = 0.7554 X 10^3 kg / m^3

The density of hot liquid sodium is:
0.84 X 10^3 kg / m^3
so that buoyancy is maintained. However, the indicator tube buoyancy is barely sufficient because in the above calculation there is no allowance for the weights of the indicator tube end spacers, the hook or the insulated top.

Note that the open steel lattice near the bottom of the primary liquid sodium pool and the fuel bundles will thermally expand vertically 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. The thermal expansion will be significant and will affect the calculation of the movable fuel bundle insertion into the matrix of fixed fuel bundles unless temperature compensating measurements are performed. Hence the overhead laser scanner may need need a compensating fixed fuel bundle elevation measurement.

The differential vertical thermal expansion per fuel bundle is approximately:
20 ppm / deg C X 430 deg C X 16.5 m = 0.1419 m
Hence it is essential that the laser scanning system cancel out vertical thermal expansion.  

The movable fuel bundle vertical travel is limited to 1.1 m by the FNR actuator design.

The hydraulic fluid feed tubes are routed through the open steel lattice. These hydraulic tubes must be sufficiently flexible to allow for +/- 0.5 m earthquake induced movement of the fuel assembly with respect to the primary pool walls.

The Indicator tubes are located on staggered lines. Along each line the center to center distance between the indicator tubes is:
42 (9 / 16) inch = 23.625 inch.

Thus the optimum buoyant sphere diameter appears to be just less than 15.0 inches.

The indicator tube OD is 8.625 inch. Hence one 23.625 inch - 8.625 inch = 15.0 inch OD buoyant sphere will barely fit on the same line between adjacent indicator tubes. Such spheres will not clash on diagonals. Thus the optimum buoyant sphere diameter appears to be just less than 15.0 inches.

Now assume that the entire sodium surface is covered by such spheres. The pool ID is:
20 m X 1 inch / .0254 m = 787.4 inch = 52.49 X 15 inch = 53 X 14.86 inch

Now assume that the buoyant spheresare actually 14.8 inch OD. Without the indicator tubes the spheres will arrange themselves woth one central sphere surounded by 26 rings of spheres. The first ring has 6 spheres, the next ring has 12 spheres, the next has 18 spheres, etc. The total number of spheres required to cover the entire sodium surfce is:
1 + 6 + 12 + 18 + 24 +...
= 1 + 6(1 + 2 + 3 + 4 ....26)
= 1 + 6 (13) (27)
= 2107

The reactor core zone is about 10 m in diameter so that absent indicator tubes the number of buoyant spheres in a single layer covering the core zone is about:
2107 / 4 = 523

However, with indicator tubes present there is only one buoyant sphere position per fixed fuel bundle position. In the central core zone the number of buoyant spheres equals the number of fixed fuel bundles. From the web page titled: FNR Geometry the number of fixed fuel bundle positions in the core zone is: 481. Thus for a single layer of buoynt spheres the required number of 14.8 inch OD spheres is about:
2107 - 523 + 481 = 2065

However, in an emergency fire suppression situation we do not know whether or not the indicator tube will be present. In a fire suppression situation we need 4 layers of buoyant steel spheres. the weight of the upper three layers will essentially submerge the fourth layer. Hence for fire suppression each FNR needs:
4 X 2107 = 8428 buoyant steel spheres, each 14.8 inch OD.

During normal times these buoyant steel spheres must be stored above the pool deck such that when released they will fall and roll into the sodium pool.

Assume that these spheres are stored in wall cabinets between adjacent pairs of NaK pipes. The center to center distance between adjacent pairs of NaK pipes is:
Pi (25 m) / 56 = 1.4025 m = 1.4025 m / (0.0254 m / inch) = 55.216 inch

The NaK pipes may be 18 inch in diameter so the remaining space is at most 55.216 inch - 18.0 inch = 37.216 inch wide. thus this space can only accommodate two ball diameters. Assume that the cabinet depth is also restricted to three ball diameters so as to not to intrude to much over the pool deck. Each cabinet can be about 11 m high which will accommodate: [11 m X 1 inch / 0.0254 m] / [14.8 inch / layer] = 29 layers of spheres. Hence each cabinet can hold:
29 layers X 6 sphere / layer = 174 spheres.

Hence 48 such cabinets can hold:
48 X 174 = 8352 spheres.

The NaK pipes will displace at least 3 X 96 = 288 spheres. Hence that wall cabinet design is sufficient for sphere storage. An angled ejector plate at the cabinet bottom causes the spheres to roll out, cross about 1.3 m of pool deck and fall into the sodium pool.

The sphere surface area is 4 Pi R^2.
The sphere mass = 4 Pi R^2 T Rho
T = surface thickness
Rho = steel density

Sphere volume = (4 / 3) Pi R^3

Hence average sphere density is:
[4 Pi R^2 T Rho] / [(4 / 3) Pi R^3]
= [3 T Rho / R]

T = (1 / 16) inch
R = 14.8 inch / 2
= 7.4 inch
Sphere density = [3 T Rho / R]
= [3 (1 / 16)inch X 7.874 X 10^3 kg / m^3] / 7.4 inch
= 199.5 kg / m^3

Four lyers of such spheres will almost submerge the bottom layer in liquid sodium.

Note that these spheres cannot be in place during normal operation because they will disturb the indicator tube related measurements.

Each floating sphere is assembled from two hemispheres. Each hemisphere is made from a sheet stainless steel disk initially about Pi R = Pi (7.4 inch) = 23.25 inch diameter. Radial slots with the desired width as a function of radius are cut using a laser cutter and then the sheet is bent around a hemispherical form. The slot edges are welded together to make the sheet steel hemisphere. Then two hemispheres are welded together to make a sphere. The sphere is filled with argon at atmospheric pressure at room temperature. The sphere must then be sealed and leak tested. The finished spheres must have a maximum diameter of 14.8 inches and a minimum diameter of 14.6 inches. As an alternative possibly a pressing operation or a spinning operation can be used to make the hemispheres.

Sphere wall stress check. At operating conditions due to high temperature the absolute pressure inside the sphere may reach 3 atmospheres so the gauge pressure may be 2 atmospheres. We can find the wall stress Sw using the formula:
2 X 14.7 psi X 14.8 inch = 2 X (1 / 16) inch X Sw
Sw = 16 X 14.7 psi X 14.8 = 3481 psi
which should be well within the metal wall stress limit.

This web page last updated November 25, 2023.

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