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

Elsewhere on this website Fast Neutron Reactors (FNRs) have been identified as the primary source of energy for meeting mankind's future energy needs. This web page focuses on the design of the FNR's primary sodium pool.

The EBR-2 primary sodium pool had no visible corrosion of its stainless steel alloy after 30 years of operation. The exact alloy is detailed in the attached file referred to as: EBR-II stainless steel alloy analysis.

The inside diameter of the primary sodium pool should be 20.0 m to allow for a 12.6 m nominal diameter reactor core, a 1.333 m wide perimeter reactor blanket, a 0.666 m wide ring for storing used active fuel bundles and a 1.7 m wide ring for intermediate heat exchangers. The primary sodium depth must be 15 m to allow 6 m high intermediate heat exchanger tubes, 6 m high fuel tubes and a 3 m guard band underneath the fuel tubes.

The bottom 3 m of the primary sodium pool is divided into a 1.5 m height for the open steel lattice and 1.5 m for the fuel bundle bottom supports. In the case of movable fuel bundles the central bottom support penetrates 1.2 m into the open steel lattice when fully withdrawn.

There are no penetrations of the primary liquid sodium pool walls or floor below the pool deck, which is 1 m above the normal sodium surface. The ball bearings, the open steel lattice, the reactor fuel assembly, the intermediate heat exchange bundle supports and the intermediate heat exchange bundles are all inserted into the primary liquid sodium pool via the top surface of the primary sodium pool.

The top surface of the liquid sodium in the pool is nominally 1 m above grade level.

The open steel lattice rests on a layer of 1.000 inch diameter ball bearings. The ball bearings form a hexagonal close packed layer. The average area occupied by each ball bearing is:
(3^0.5 / 2) inch^2 = 0.8660 inch^2


By comparison the cross sectional area of the ball beating is:
Pi (1 / 2 inch)^2
= 0.785 inch^2

The number of ball bearings required to cover a disc 17.5 m diameter is:
Pi (17.5 m / 2)^2 / (.0254 m / inch)^2 X 1 bearing / 0.8660 inch^2
= 1,722,030

The fuel bundles have an overall height of 7.9 m. To relocate a fuel bundle it must be lifted about 8.0 m to clear other fuel bundles. When lifted the top 2.4 m are above the primary sodium surface.

There must be adequate room for primary sodium natural circulation. At the primary sodium pool perimeter the available cross sectional area is:
Pi [(10 m)^2 - (8.3 m)^2]
= 31.11 Pi m^2

For radial flow between the open lattice and the fuel tube bottoms the cross sectional area is:
Pi (2)(8.3 m)(1.5 m)
= Pi (24.9 m^2)___________

Thus about 0.5 m of the open steel lattice height must be truly open to allow adequate radial primary sodium natural circulation._________

The nominal primary sodium volume is:
Pi (10 m)^2 (15 m) = 1500 Pi m^3
= 4712 m^3

The primary sodium that is displaced by solid items within the primary sodium pool is approximately offset by the volume of the secondary sodium.

Below the pool deck the primary liquid sodium pool wall and bottom consist of three upright flat bottom nested stainless steel cups separated by 1 m thicknesses of fire brick between the adjacent cups. The fire brick will retain its shape and dimensions over the long term thus preventing pool wall shape distortion potentially related to use of silica sand instead of fire brick for intercup separation.

The fire brick provides thermal insulation and also acts as a gamma ray shield.

The innermost stainless steel cup is 20 m diameter X 16 m deep. The middle stainless steel cup is 22 m diameter X 17 m deep. The outermost stainless ssteel cup is 24 m diameter X 18 m deep.

This nested cup configuration is shown on the following FNR side elevation diagram.

This nested steel cup design faces a number of engineering challenges including: a) Operating hoop stress;
b) Thermal expansion;
c) Field welding;
d) Bottom top surface grinding;
e) Bottom bearing surround;
f) Seal testing;
g) Potential sodium absorption by fire brick;
h) Corrosion prevention;

The corrosion of stainless steel by liquid Na as reported by the EBR-2 experiment was negligibly small. However, we do not have good information with respect to the temperature and impurity concentration in the EBR-2. Here is a reference relevant to corrosion of various steels by caustic soda.

In the event that the two inner steel cylinders fail the FNR geometry must be such that fission product decay heat can still be removed from the FNR. Hence the primary sodium inlets feeding the intermediate heat exchangers and part of the heat exchanger tube length must remain below the liquid sodium surface.

The fire brick provides thermal insulation and will not react with the hot liquid sodium in the event of an inner cylinder leak. The density of the fire brick is chosen to ensure that in the event of leaks in both of the inner two steel cups the liquid sodium level in the primary sodium pool will remain sufficient to allow reliable extraction of fission product decay heat via the intermediate heat exchangers.

Fine sand has a density of 1.60 kg / lit. The same sand saturated with water has a density of 2.01 kg / lit. Thus if liquid sodium seeps into the dry sand the volume of liquid sodium that can potentially be absorbed is 0.41 lit Na / lit fine dry sand.

For comparison the fractional unfilled volume in a stack of spheres is: (8 - (4 / 3) Pi) / 8 = 0.476

The volume of fire brick between the side walls below the 11 m mark is:
Pi [(12 m)^2 - (10 m)^2] 11 m
= Pi (484 m^3)

The volume of sodium potentially absorbed by the fire brick in the side walls is:
Pi (484 m^3) (0.476) = Pi (230.4 m^3)

The volume of fire brick between the cup bottoms is:
Pi (2 m) (12 m)^2 = Pi (288 m^3)

Assume that the volume of sodium absorption by fire brick is:
0.476 lit sodium / lit fire brick

Then the maximum possible sodium absorption by the fire brick between the cup bottoms is:
Pi (288 m^3)(0.476) = Pi (137.1) m^3

Thus the volume of liquid sodium that can potentially be absorbed by the fire brick is:
Pi (137.1 + 230.4) m^3 = Pi (367.4) m^3

Note that Pi (367.4) m^3 < Pi (400) m^3
which implies that even if both the innermost cup and the middle cup fail the liquid sodium level in the inner most cup will drop less than 4.0 m.

The fire brick used in this application should have low thermal conductivity. The issue of fire brick thermal conductivity is discussed in the Stack Thesis.

The density of fire brick is 1.6 X the density of water. The ratio of the fire brick thickness to 30 cm of lead is:
2 m / 0.30 m = 6.66

Hence if the fire brick was compressed into a layer 30 cm thick its density would be:
6.66 X 1.6 = 10.656 gm / cm^3

In addition there is the weight of steel. There are 3 layers of steel, each (3 / 4) inch thick for a total of (9 / 4) inches. The density of steel is about:
7.874 gm / cm^3.

Thus the shielding mass of the steel is:
(9 / 4) inch X 2.54 cm / inch X 7.874 gm / cm^3 = 45.0 gm / cm^2

Distributing this additional mass over a 30 cm thickness gives an additional shield material density of:
45.0 gm / cm^2 / 30 cm = 1.5 gm / cm^3

Thus the equivalent shield material density is:
10.656 gm / cm^3 + 1.5 gm / cm^3 = 12.156 gm / cm^3

This is more than the density of lead which is: 11.36 gm / cm^3

Hence a 2 m thickness of fire brick plus 3 X (3 / 4) inch steel is a better gamma ray shield than is a 30 cm thickness of lead.

The sheet steel cups must be sufficiently strong that they can safely withstand the worst case hydraulic heat issues of liquid sodium with fire brick.

At the bottom of the inner most nested stainless steel cup there is a 15 m head of liquid sodium.

The density of the liquid sodium is about 927 kg / m^3

The acceleration of gravity is about 9.8 m / s^2

Hence the static head pressure at the bottom of the pool is given by:
15.0 m X 927 kg / m^3 X 9.8 m / s^2 = 136,269 Pa

On a 1 m high strip of inner cup side wall this pressure exerts a force of:
1 m X 20 m X 136269 Pa = 2,725,380 Newtons.

Let W = inner most cup wall thickness.

Then the hoop streess on the inner most cup wall material near the bottom of the primary liquid sodium pool is:
(2,725,380 Newtons) / (2 X W X 1 m) = (1,362,690 / W) Pa
where W is in m.

The maximum allowable working stress for stainless steel at 500 degrees C is:
10,000 psi X 101,000 Pa / 14.7 psi = 68,707,483 Pa

Hence the smallest allowable value of W is given by:
W = 1,362,690 / 68,707,483 = 0.0198 m
= 0.0198 m / .0254 m /inch
= 0.7808 inch
which indicates that near the bottom of the inner most cup the wall must be composed of 3 / 4 inch thick low carbon stainless steel.

For practical field fabrication the walls of each nesting cup are made of ~ 20 X ~ 3 m X (3 / 4) inch vertical strips with 2 m long bottom pieces preattached. These strips are pre-rolled to provide the required 10 m radius of curvature. These strips are prefabricated for shipping and have beveled edges for field welding. The wall strip lengths are 16 m, 17 m and 18 m. The bottom of each cylinder is made from 20 triangular plates cut from 3 m X 8 m X (3 / 4) inch steel sheets. The tops of the pool side wall strips have holes for lifting. The heaviest single pool wall component is:
20 m X 3 m X 0.75 inch X .0254 m / inch X 7.85 g / cm^3 X 10^6 cm^3 / m^3 X 1 kg / 1000 g X 1 tonne / 1000 kg
= 8.97 tonnes

Thus a crane with a 10 tonne lifting capacity is required at the reactor site for primary sodium pool assembly. The gantry crane with one enclosure end wall not yet installed should be adequate for this purpose.

The pool wall outside surface area is:
Pi (18 m) 2 (12 m) + Pi (12 m)^2
= Pi (12 m) (48 m)
= Pi (576 m^2)

The thermal conductivity of sand is in the range:
0.15 W / m-deg C to O.27 W / m-deg C

The maximum heat loss via thermal conduction through the pool walls and floor is:
Pi (576 m^2) X 0.27 W / m-deg C X 505 deg C X (1 / 2 m)
= 123,366 Wt
= 123.4 kWt

The FNR primary pool needs 50 kW of immersion heater capacity for liquid sodium melting at startup. This heat may be applied by one or more of the secondary sodium loops. Note that it is impossible to install or remove any fuel bundles until after the primary liquid sodium has completely melted.

The thermal coefficient of expansion of stainless steel is:
17 um / m deg C

Thus the radial expansion of the innermost cup in transitioning from 15 deg C to 500 deg C is:
485 deg C X 17 X 10^-6 / deg C X 10 m = 0.0824 m ~ 8 cm.

The corresponding radial expansion of the second cup will be about 4 cm.

This 4 cm of differential expansion must be absorbed by gaps between the fire bricks and the nested steel cups.

The pool liner side walls will also vertically expand:
505 deg C X 17 X 10^-6 / deg C X 16.0 m = 0.137 m
Thus the hot pool deck must be free to move up and down with respect to adjacent cool walls.

The walls above the pool deck will vertically expand by:
505 deg C X 17 X 10^-6 / deg C X 14 m = 0.12 m

Hence the fiber ceramic insulation between the pool enclosure metal ceilings must compress by:
.137 m + .12 m = 0.257 m or 25.7% insulation compression.

The pool deck is rigidly welded to the inner nesting cup. Hence the fiber ceramic in the walls above the pool deck must accommodate pool deck radial expansion of about 9 cm or 9% insulation compression.

On top of the exposed fire brick is a sheet steel pool deck. The pool deck is welded to the inner most stainless steel nested cup and slides over the other two stainless steel nested cups to permit stress free thermal expansion and contraction.

On top of the inner most cup bottom is a sheet steel layer which protects the underlying stainless steel cup bottom from accidental damage.

On top of this protective sheet is a 1.5 m high open steel lattice which supports all the fuel bundles and contains the 340 hydraulic actuators and related liquid sodium hydraulic pressure tubes for the mobile fuel bundles.

Inside the pool and around its perimeter are steel columns which support the intermediate heat exchangers.

At the bottom of the steel lattice is a layer of solid B4C spheres_________ whose function is to prevent bits of melted reactor fuel from forming a critical mass. Note that these B4C spheres are outside the neutron flux and hence will not form C-14.

Underneath the outermost cylinder bottom is 1 m thick space set by a row of steel I beams which rest on the concrete foundation and support the primary sodium pool and its contents.

Outside the outer cup wall is a > 1 m wide air gap for air cooling and for maintenance access to the below pool ventilation space. Within the air gap between the outer stainless steel pool wall and the concrete wall inner face are structural steel radial elements which stabilize the outer pool wall. In the event of inner and middle nested steel cup failures this structural steel relieves hoop stress in the outer nested cup steel wall.

The area of the stainless steel sheet forming the primary sodium pool outside bottom is:
Pi (12 m)^2 = 452.4 m^2

The area of the stainless steel sheet forming the primary sodium pool outside wall is:
Pi (24 m) (18 m)
= 1357.2 m^2

Primary sodium pool outer stainless steel wall total area is:
452 m^2 + 1357.2 m^2 = 1809.6 m^2

The area of the stainless steel sheet covering the primary sodium pool inside bottom is:
= Pi (10 m)^2
= 314.2 m^2

The area of the stainless steel sheet covering the primary sodium pool inside walls is
Pi (20 m) (16 m)
= 1105.3 m^2

Total inner liner area is:
314.2 m^2 + 1105.3 m^2 = 1419.5 m^2

The area of stainless steel sheet metal covering the primary sodium pool pool deck is:

= Pi (12.0^2 - 10.0^2) m^2
= 138.2 m^2

The pool floor must be well supported because it carries the entire weight of the liquid sodium plus the weight of the fuel bundles and their control rod apparatus plus the weight of the sodium piping plus the weight of the fuel bundles in storage plus the weight of the pool walls and floor, including the 2 m thickness of fire brick insulation.

After pouring the concrete foundation slab the straight concrete walls are erected first. Then the pool liners and fire brick are installed.

Consider the earthquake acceleration and displacement that are necessary to cause the primary liquid sodium level to rise 1 m on one side of the pool and drop 1 m on the other side of the pool. This situation corresponds to a sustained horizontal acceleration of about 0.1 g.

There may be merit in installing a removable 4 m high "slosh wall" on top of the primary sodium pool to confine sloshing liquid sodium in the event of an earthquake induced horizontal acceleeration of up to about 0.5 g. The pipe penetrations of the slosh wall do not require perfect sealing because they are only briefly exposed to the liquid sodium in rare situations.

The primary sodium pool half fills a vertical cylinder 20 m diameter X 30 m high. Normally the sodium surface is horizontal. Consider an horizontal earthquake acceleration that causes the sodium surface to be an inclined plane stretching from a bottom corner of this cylinder to an opposite top corner of this cylinder.

The height of this incline is 30 m. The base of this incline is 20 m. A little geometry shows that it takes a sustained 1.5 g horizontal acceleration to cause the liquid sodium surface to adopt this inclined shape.

A earthquake induced 1.5 g vertical acceleration causes a maximum vertical acceleration of 2.5 g. This is about the structural limit of normal engineered structures. Thus the primary sodium pool can reasonably be rated for public safety at up to 1.5 g earthquake induced vertical accelerations.

Note that there are no wall penetrations at wall heights normally exposed to liquid sodium. At wall heights where there are wall penetrions for pipes and air locks the exposure to hot sloshed liquid sodium is only transient and is extremely rare.

The pool ceiling, which carries the gantry crane and monitoring system, is not intended to withstand even sloshed liquid sodium. Hence an earthquake acceleration of greater than 1.5 g will likely result in a facility repair shutdown for an extended period.

This web page last updated July 13, 2021.

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