XYLENE POWER LTD.

FNR BUOYANT STEEL SPHERES

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

BUOYANT STEEL SPHERES:

The buoyant steel spheres must be of a size thatwill easily fit between adjacent indicator tubes.

The spheres must lend themselves to storage in side wall cabinets or in the dome roof space.

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.
 

BUOYANT SPHERES:
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. However, along each diagonal line the center to center distance is:
2^0.5 X 21 (9 /16) ich = 16.705 in

The indicator tube OD is: 8.625 inch

Hence the maximum sphere diameter for the spheres to slide between indicator tubes is:
16.705 inch - 8.625 inch = 8.080 inch

Thus the buoyant spheres must be 8.0 inch diameter.

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 = 99 X 7,9535 inch

Without the indicator tubes the spheres will arrange themselves woth one central sphere surounded by 49rings 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 ....49)
= 1 + 6 + 6(24)(51)
= 7351

For fire suppresion we will need about 5 layers x 7351 spheres/ layer = 36,755 buoyant spheres.

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 5 layers of buoyant steel spheres. The weight of the upper four layers will essentially submerge the bottom layer. Hence for fire suppression each FNR needs:
5 X 7351 = 36,755 buoyant steel spheres, each 8 inch OD.

During normal times these buoyant steel spheres must be stored in wall cabinets 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 16 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 four sphere diameters. Assume that the cabinet depth is also restricted to four 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] / [8 inch / layer] = 55 layers of spheres. Hence each cabinet can hold:
55 layers X 16 spheres/ layer = 880 spheres.

Hence 44 such cabinets can hold:
44 X 880 = 38,720 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 the pool deck and fall into the sodium pool.

SPHERE BUOYANCY:
The sphere surface area is 4 Pi R^2.
The sphere mass = 4 Pi R^2 T Rho
where:
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]

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.
 

SPHERE FABRICATION:
Each floating sphere is assembled from two hemispheres. Each hemisphere is made from a sheet stainless steel disk initially about Pi R = Pi (4 inch) = 12.56inch 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 8.0 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 Pi X (4 inch)^2 = Pi X 8 inch X (1 / 32) inch X Sw
or
Sw = 8 X 14.7 psi X 16 = 1882 psi
which should be well within the metal wall stress limit.
 

This web page last updated May 29, 2025.