XYLENE POWER LTD.

FNR SODIUM POOL

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

INTRODUCTION:
Elsewhere on this website sodium cooled Fast Neutron Reactors (FNRs) have been identified as the primary source of sustainable and dependable power for meeting mankind's future energy needs. This web page focuses on the design of the FNR's sodium pool. An important function of this pool is to provide physical protection for the fuel assembly.
 

SODIUM POOL DESCRIPTION:
The sodium pool consists of three nested stainless steel cups separated from one another by 1 m thicknesses of granular insulating filler material (fire brick, silica sand or NaF) with a fill factor of at least 50%.
The inner nested steel cup is 20 m diameter X 16 m deep;
The middle nested steel cup is 22 m diameter X 17 m deep;
The outer nested steel cup is 24 m diameter X 18 m deep;

Fire brick is used between the nested cup bottoms to avoid possible system buoyancy issues if the average density of the sand is too great.
 

The fire brick and sand filler material must not chemically react with or dissolve in hot liquid sodium and must not react with stainless steel. Posssible filler materials are NaCl (Rho = 2.16 X 10^3 kg / m^3) and/or NaF (Rho = 2.78 X 10^3 kg / m^3). The density of the filler material might be important because in the long term the inner and middle cups might float on their surrounding insulation material. The fill factor is important because it must be sufficient to prevent the sodium level dropping too much in the event of inner and middle nested steel cup failures.

The granular filler material also enables differential thermal expansion between the inner, middle and outer nested steel cups without causing undue thermal stress. The pool deck overlaps the inner cup and is slightly sloped toward the inner cup to provide drain back of sodium vapor condensate to the sodium pool and to assist the rolling of buoyant metal balls used for sodium fire asphixiation.

The sidewall plates forming the inner cup have welded reinforced inside brackets that stabilize the intermediate heat exchange bundles. The intermediate heat exchange bundles must radially slide as well as rotate on to accommodate radial pipe thermal expansion and contraction and rotation for pipe flange alignment.

The required stainless steel plate thickness is derived from hoop stress calculations. Note that the hoop stress is largest in the outer cup.
 

KEY SODIUM POOL FEATURES:
a) The sodium pool must reliably and permanently contain the liquid sodium at 100 deg C to 500 degrees C under a variety of adverse conditions;

b) The sodium pool must reliably dump excess heat including fission product decay heat;

c) The sodium pool must reliably exclude water.

d) The sodium pool elevation must allow for an unplanned rise in the water table and unplanned grade level flooding.

e) The recommended elevation of top of sodium pool is 2 m above grade and 19 m above the highest normal water table.

f) There should be a 3 m wide neutron absorbing sodium guard band between the outside of the FNR fuel assembly and the sodium pool's bottom and walls;

g) The sodium pool inner wall must physically stabilize the posts supporting the intermediate heat exchange bundles with appropriate provisions for sodium pool and radial pipe thermal expansion and contraction;

h) For sodium containment certainty the sodium pool consists of three nested steel cups, each of which can by itself reliably contain the sodium;

i) Between the inner cup and the middle cup is a 1 m thickness of fire brick on the bottom and sand on the sides;

j) Between the middle cup and the outer cup is a 1 m thickness of fire brick on the bottom and sand on the sides.

k) Each cup is cylindrical. The outer cup is 24 m dia X 18 m high. The middle cup is 22 m dia X 17 m high. The inner cup is 20 m dia X 16 m high.

l) In the event of failures of the inner and middle nested cups the sodium top surface must not drop so far that fission product decay heat can not be readily removed via the 6 m high intermediate heat exchange bundles. The minimum required fill factor by the sand and fire brick is 50%.

m) It must be practical to move an active fuel bundle from the reactor core to a cooling position on the fuel assembly perimeter without lifting the fuel bundle's core or blanket rods above the top surface of the liquid sodium pool. This requirement sets an overall lengthconstraint on the fuel bundles.

n) The sodium pool must be field assembled from factory formed modules;

o) The dimensions of the individual modules used to form the sodium pool must be consistent with road truck and rail transport.

p) The sodium pool walls must provide sufficient insulation that under normal circumstances heat loss out the sides and bottom of the sodium pool is minimal.

q) The inner and middle cup pieces are fabricated from 0.75 inch thick sheet steel. The outer cup is fabricated from 1.00 inch thick sheet steel.

r) The floors of the nested steel cups are each formed from 28 pie shape flat sheet steel pieces. Each piece subtends an angle of:
360 deg / 28 = 12.85714 degrees.
For the outer cup the bottom radius is 12 m, for the middle cup the bottom radius is 11 m and for the inner cup the bottom radius is 10 m.

s) The side walls of each cup are formed from flat pieces that have been rolled to have the appropriate radius of curvature. For the outer cup the side piece height is 18 m and the width is 2 (12 m) Pi / 28 =2.6928 m and the radius of curvature is 12 m. For the middle cup the side piece height is 17 m, the width is 2 (11 m) Pi / 28 = 2.4684 m and the radius of curvature is 11 m. For the inner cup the side piece height is 16 m, the width is 2 (10 m) Pi / 28 = 2.2440 m and the radius of curvature is 10 m.

t) The total welded joint length for the outer cup is: 28 (12 m) + 28(18 m) + 2 (12 m) Pi = 1195.4 m.
The total welded joint length for the middle cup is: 28 (11 m) + 28 (17 m) + 2 (11 m) Pi = 853.1 m
The total welded joint length for the inner cup is: 28 (10 m) + 28 (16 m) + 2 (10 m) Pi = 790.8 m

Total field weld joint length for all three nested cups is:
1195.4 m + 853.1 m m + 790.8 m = 2839.3 m

u) At the middle of each cup bottom is a small disk that connects together the narrow ends of the pie shaped bottom plates.

v) The fire brick and sand must provide sufficient thermal insulation that under normal circumstances heat loss out the sides and bottom of the sodium poolis minimal.

w) The volume of fire brick inside the outer cup and supporting the middle cup is:
Pi (12 m)^2 (1 m) = 452.4 m^3
The volume of fire brick inside the middle cup and supporting the inner cup is:
Pi (11 m)^2 (1 m) = 380.1 m^3

x) The volume of sand between the outer cup and the middle cup is:
[Pi (12m)^2 - Pi (11 m)^2] (12 m) = 867.1 m^3 sand
On top of the sand is:
[Pi (12m)^2 - Pi (11 m)^2] (5 m) = 361.3 m^3 fibrefrax.
The volume of sand between the middle cup and the inner cup is:
[Pi (11 m)^2 - Pi (10 m)^2] (16 m) = 1005.6 m^3 sand

y) The outer cup is supported by a layer of I beams each 1 m wide X 1 m high. These I beams provide both bottom ventilation and service access. The total I beam length requirementis 24 m X 24 = 576 m. These I beams are delivered in 48 X 12 m lengths. At each end of the I beams are cooling air manifolds.

z) The maximum sodium volume is:
Pi (10 m)^2 (15 m) = 4712.4 m^3. This volume is reduced by the volumes of the fuel assembly, open steel lattice, intermediate heat exchangers and intermediate heat exchanger supports.
 

SODIUM POOL MAJOR DIMENSIONS:
The inside diameter of the sodium pool should be 20.0 m to allow for a 11.4 m nominal diameter reactor core, a 1.20 m wide perimeter reactor blanket, a 0.60 m wide ring for storing used active fuel bundles, a circular 1.8 m wide fuel bundle movement path and a 1.7 m wide perimeter ring for intermediate heat exchangers. The 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 liquid sodium 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 pipe penetrates 1.2 m into the open steel lattice when fully withdrawn.

There must be vertical allowance for the open steel lattice bottom suppport layer of ball bearings and the smooth steel sheets above and below the ball bearings.

There are no penetrations of the 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 and the intermediate heat exchange bundles are all inserted into the liquid sodium pool via the top surface of the sodium pool.

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

The sodium pool is assembled using the polar gantry crane at a time when there is still a sufficient sidewall openning in the pool enclosure at the airlock position to admit the pool modules.

Once assembled the sodium pool is permanent. There is no provision to replace the sodium pool at any time during the reactor working life. Should it need repair it can be field patched. The sodium pool walls and floor are protected by sufficient thicknesses of sodium (and gadolinium) that their neutron exposure should be negligible. However, the pool liner (the inner steel cup) is subject to continuous exposure to 400 to 500 degree C sodium.
 

SODIUM POOL WALL MATERIAL:
The EBR-2 sodium pool had no visible corrosion of its stainless steel alloy after 30 years of operation. The corrosion of stainless steel by liquid Na, as reported by the EBR-2 experiment, was negligibly small. The exact alloy is detailed in the attached file referred to as: EBR-II stainless steel alloy analysis. 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.
 

When air is excluded the common stainless steels 304 and 316 are believed to be long term thermally stable at 460 degrees C .

Web sites dealing with stainless steel indicate that its corrosion resistance decreases after prolonged exposure to temperatures greater than 425 degrees C. In this respect 316 SS is believed to be significantly more corrosion resistant than 304 SS. Since the sodium pool is extremely difficult to replace it should be formed from 316L SS. Note that 316L SS is slightly more expensive than 304L SS. TheLis important for weldability.

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.
 

GANTRY CRANE REQUIREMENT:
The gantry crane must be able to lift the largest single sodium pool component. The outter cup sidewall plates are 18 m X 2.6928 m. If these plates are 0.75 inch thick then each one weighs:
18 m x 2.6928 m m X 0.75 inch X .0254 m / inch X 7.874 X 1000 kg / m^3
= 7271 kg
= 7.271 tonnes

If the plate is 1.00 inch thick this single plate weight rises to:
18 m x 2.6928 m m X 1.00 inch X .0254 m / inch X 7.874 X 1000 kg / m^3
= 9694 kg
= 9.694 tonnes

Hence, the polar gantry crane must be rated for lifting at least 10 tonnes.
 

WELD LEAKAGE:
The reason for having three nested cups is to ensure that liquid sodium will never leak out and water will never leak in.
If water enters the space between the outer and the middle cups or if sodium enters the space between the inner and the middle cups then the reactor should be shut down for pool repair at the next opportunity.

If the inner and middle cups both fail liquid sodium will fill the gas spaces in the inter-cup filler. That will cause the elevation of the liquid sodium pool surface to drop by about 4 m. Hence the bottom 2 m of the intermediate heat exchange bundles will remain immersed in liquid sodium, which is enough to remove fission product decay heat.

However, if due to a further failure of the outer steel cup the sodium surface elevation continues to drop, that circumstance is very dangerous because:
a) As the sodium surface drops below the intermediate heat exchange bundles heat removal will stop;
b) Fission product decay heat will keep raising the temperature of the fuel and the remaining liquid sodium;
c) Eventually the high fuel temperature will cause fuel melting, which should be confined by the fuel tubes;
d) Eventually the liquid sodium temperature will reach its boiling point causing high pressure sodium vapor emission;
e) When due to sodium boiling the sodium surface drops to the level of the fissile fuel rods the reactor reactivity will increase which will cause a rapid reactor setpoint temperature increase if the fissile fuel geometry is otherwise unchanged. This setpoint temperature increase will cause fuel melting even if there is little or no fission product decay heat.

The bottom line is that until the movable fuel bundles are withdrawn from the matrix of fixed fuel bundles it is crucial to ensure that the sodium pool level is maintained and that there is always sufficient redundant cooling by natural NaK circulation to reject fission product decay heat. Hence, from a walkaway safety perspective it is essential that the sodium pool consist of three nested steel cups that are spaced such that the largest possible sodium surface elevation drop is 4 m.
 

CONTAINED VOLUMES:
Consider the top 4 m in the sodium pool. The associated volume is about:
4 m (Pi) (10 m)^2 = 400 Pi m^3 = 1256.6 m^3

The contained filler volume between the inner and middle nesting cups below the potentially lowered sodium level is:
Pi (11 m)^2(1 m) + Pi [(11 m)^2 - (10 m)^2](12 m)
= Pi[121 m^3 + 21 m^2 (12 m)]
= Pi [373 m^3]

The contained filler volume between the middle and outer nesting cups below the potentially lowered sodium level is:
Pi (12 m)^2(1 m) + Pi [(12 m)^2 - (11 m)^2](13 m)
= Pi [144 m^3] + Pi (23 m^2) 13 m]

Assuming that the filler occupies 50% of the volume, the volume of sodium that could be absorbed is:
Pi[373 m^3 + 443 m^3] / 2 = Pi[816 m^3 /2] = 1281.8 m^2.
Hence we must be certain that the fire brich and sand fill factor is at least 50%.

If the inner cup and the middle cup walls both fail the liquid sodium level in the inner cup will drop by slightly more than 4.0 m.
 

GRANULAR FILLER VOLUMETRIC CONSTRAINT:
For comparison the fractional unfilled volume in a stack of spheres is:
(8 R^3 - (4 / 3) Pi R^3) / 8 R^3 = 0.476
 

SODIUM VAPOR PRESSURE:

Temperature Deg K	Pressure MPa
400	1.8 X 10^-10
500	8.99 X 10^-8
600	5.57 X 10^-6
700	1.05 X 10^-4
800	9.41 X 10^-4
900	5.137 X 10^-3
1000	1.995 X 10^-2
1100	6.016 X 10^-2

Note that above a sodium surface temperature of about 800 degrees K we have to be concerned about the effect of sodium vapor pressure on the sodium pool enclosure walls which are likely rated for ~ 10^-3 MPa above the outside air ambient pressure.
 

OPTIONAL BALL BEARING LAYER:
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 bearing is:
Pi (1 / 2 inch)^2
= 0.785 inch^2

FUEL BUNDLE CLEARANCE ISSUES:
The fuel bundles have an overall height of 8.0 m. To relocate a fuel bundle it must be lifted about 8.0 m to clear other fuel bundles. When so lifted the top 2.4 m of the fuel bundle are above the liquid sodium surface.

There must be adequate room for liquid sodium natural circulation. At the sodium pool perimeter the available cross sectional area is:
Pi [(10 m)^2 - (7.0 m)^2]
= 51 Pi m^2

The area occupied by the intermediate heat exchange bundles is:
48 Pi (0.5 m)^2 = 12 Pi m^2
Hence the actual perimeter open area is:
51 Pi - 12 Pi = 39 Pi m^2
This area is required to provide the sodium circulation required to raise the return temperature from 340 C to 400 C.

At he outer perimeter of the core zone the cross sectional area available for sodium circulation is:
Pi (10 m)(3 m) = 30 Pi m^2

Thus when the reactor is operational the 3 m underneath the fuel assembly must be truly open to allow adequate radial sodium natural circulation.
 

POOL WALL CONSTRUCTION:
Below the pool deck the liquid sodium pool wall and bottom consist of three upright nested stainless steel cups separated from one another by 1 m thicknesses of insulating dry filler between adjacent cups. The filler density and filler sidewall height are chosen so that the inner cup floats on the filler between the inner and middle cups. The filler density and height are chosen so that the middle cup almost floats on the filler between the middle and outer cups. Then the cups will retain their shape, dimensions and separation over the long term. It may be necessary to use rigid spacers to set the cup separations at the top edge.

In normal operation for the inner cup and the middle cup the filler head pressure should balances the liquid sodium head pressure plus the cup weight. This configuration reduces the cup material hoop stress, except for the outer cup. Hence the outer cup is 1.00 inch SS, the middle cup is 0.75 inch SS and the inner cup is 0.75 inch SS.

The granular filler should remain loose and liquid like so that as the distance between nested stainless steel cup walls changes due to thermal expansion and contraction and as the filler volume changes due to thermal expansion and contraction the filler level between the side walls rises or falls to provide stress relief. Possibly the granular filler material should be prefired to get rid of volatile components that might lead to filler particles sticking together. Consider use of filler composed of NaCl or NaF or a mix of these materials. Ideally the average density of the filler should be greater than the average density of the liquid sodium so as to provide balancing counter pressure to the liquid sodium plus the fuel assembly and heat exchange bundle weight.

The granular filler material also provides thermal insulation and acts as a gamma ray shield.

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) Multi-dimensional hoop stress;
b) Field welding;
c) Weld inspection;
d) Seal testing;
e) Long term weld failure prevention;
 

THERMAL CONDUCTIVITY:
The filler used in this application should have low thermal conductivity. The issue of filler thermal conductivity is discussed in the Stack Thesis.
 

GAMMA SHIELDING:
The density of NaCl filler with gas spaces is ~ 1.08 X the density of water.

On a per unit area basis the shielding provided by the filler is:
200 cm X 1.08 gm / cm^3 = 216 gm / cm^2

In addition there is the weight of steel. There are 3 layers of steel, (1 X 0.75 inch thick, 1 X 0.5 inch thick, 1 X 1.25 inch thick) for a total of 2.5 inches. The density of steel is about:
7.874 gm / cm^3.

Thus the shielding provided by the steel is:
2.5 inch X 2.54 cm / inch X 7.874 gm / cm^3 = 50.0 gm / cm^2

Hence under normal circumstances the total gamma shielding provided by the sodium pool wall is:
216 + 50 = 266 gm / cm^2

However, if the filler is NaF granules instead of NaCl granules its average density will be about:
(2.78 gm / cm^3) / 2

The resulting filler gamma shielding will be:
2.78 gm / cm^3 X (1 / 2) X 200 cm = 278 gm / cm^2

Hence the total gamma shielding will be about: 278 gm / cm^2 + 50 gm / cm^2 = 328 gm / cm^2

By comparison the density of lead is 11.343 gm / cm^3. Hence 30 cm of lead provides gamma shielding of:
30 cm X 11.343 gm / cm^3 = 340.3 gm / cm^2

Hence a 2 m thickness of NaF filler plus 2.5 inch steel is a comparable gamma ray shield to a 29 cm thickness of lead.
 

WALL HOOP STRESS:
Consider the case of sodium in the inner pool but no wall filler between the inner and middle cups.

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 = 68.7 MPa

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 maximum static head sodium pressure at the bottom of the inner cup is given by:
16.0 m X 927 kg / m^3 X 9.8 m / s^2 = 145.3 kPa

At this point the radius of curvature is: 10 m

Let W = inner most cup wall thickness.

Then if no filler is present the hoop stress on the inner most cup wall material at the weld is:
145.3 kPa X (10 m ) / (wall thickness)
= 145.3 kPa X 10 m / (0.75 inch X 0.0254 m / inch)
= 76,301 kPa X 14.7 psi / 101 kPa
= 11,105 psi

This stress is OK because the bottom of the side walls is stress relieved by:
a) A normal Na height of 15 m rather than 16 m;
b) The weld to the bottom of the inner cup provides bottom stress relief;
c) Filler sand between the inner and the middle cups.

The middle cup material thickness of 0.75 inch is OK because the filler pressure acts on both sides of it.
 

OUTER CUP HYDRAULIC HEAD ISSUES:
In normal operation between the middle cup and the outer cup the filler height is 13 m. The top 5 m are filled with fibrefrax. In normal operation the average filler density is:
2.78 / 2 = 1.39 X 10^3 kg / m^3.

The corresponding sand pressure at the bottom is:
13 m X 1.39 X 10^3 kg / m^3 X 9.8 m / s^2
= 177.1 kPa

Assume that the outer steel thickness is:
1.00 inch X 0.0254 m / inch = 0.0254 m m

With 1.00 inch thick outer steel the hoop stress is:
[12 m / 0.0254 m] X 177.1 kPa
= 83,669 kPa
= 83,669 kPa X 14.7 psi / 101 kPa
= 12,177 psi

This is OK because: a) The hoop is reinforced onthe bottom by the weld to the bottom plate;
b) the material is near room temperature;

The outer cup must be sufficiently strong that it can safely withstand the worst case hydraulic head issues of liquid sodium with filler. In the worst case liquid sodium mixes with NaF filler to give a liquid with an average density of:
(2.78 + 0.93) / 2 = 1.855
Under these circumstances the maximum liquid head is:
17 m - 4 m = 13 m

The corresponding head at the bottom is: 13 m giving a pressure of:
13 m X 1.855 X 10^3 kg / m^3 X 9.8 m / s^2
= 236.33 kPa

Assume that the outer steel thickness is:
1.00 inch X 0.0254 m / inch = 0.0254 m m

With 1.00 inch thick outer steel the hoop stress is:
[12 m / 0.0254 m] X 236.33 kPa
= 111,652 kPa
= 111,652 kPa X 14.7 psi / 101 kPa
= 16,250 psi

This calculation is only valid if the filler between the middle and outer cups acts like a liquid,
In reality when the liquid sodium reaches the outer cup it will partially freeze, so liquid like calculations will no longer be valid.
 

THERMAL CONDUCTION:
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 dry filler 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
 

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

THERMAL EXPANSION:
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 = 8.2 cm.

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

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 1 m thick 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 1 m thick walls above the pool deck must accommodate pool deck radial expansion of about 9 cm or 9% insulation compression.
 

POOL DETAILS:
On top of the exposed filler is a sheet steel pool deck. The pool deck is welded to the inner most stainless steel nesting cup and slides over the other two stainless steel nesting 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 the ball bearing layer and then the 1.5 m high open steel lattice which supports all the fuel bundles and contains the 340 actuators and related liquid sodium hydraulic pressure tubes for the movable fuel bundles.

Inside the pool and around its perimeter are reinforced steel brackets which support the intermediate heat exchange bundles.

At the bottom of the open steel lattice is a layer of solid B4C spheres which act as ball bearings and have the secondary function of preventing 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 nested steel cup bottom is 18 m diameter 1 m high space set by a row of steel I beams which rest on the concrete foundation and support the sodium pool and its contents. The outside 3 m of sodium pool radius need further support.
 

CONNECTION TO SODIUM POOL ENCLOSURE:
Below the pool deck and outside the outer cup wall is a 2.5 m wide air gap for air cooling and for maintenance access to the below pool space. Within the air gap between the outer stainless steel cup 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.
 

POOL STEEL APPROXIMATE QUANTITIES:
The area of the stainless steel sheet forming the sodium pool outer cup bottom is:
Pi (12 m)^2 = 452.4 m^2

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

Sodium pool outer cup total surface area is:
452 m^2 + 1357.2 m^2 = 1809.6 m^2

The area of the stainless steel sheet forming the sodium pool middle cup bottom is:
Pi (11 m)^2 = 380.1 m^2

The area of the stainless steel sheet forming the sodium pool middle cup wall is:
Pi (22 m) (17 m)
= 1175.0 m^2

Sodium pool middle cup stainless steel total area is:
380.1 m^2 + 1175.0 m^2 = 1555.1 m^2

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

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

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

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

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

The filler supporting the sodium inside cup floor must flat 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 sand insulation. Note that until the sodium is present the inner cup wall may be subject to severe compressive stress by the filler..
 

After pouring the concrete foundation slab the straight concrete walls are erected first. Then the roof and gantry crane, Then the pool cups are fabricated and the filler is installed.
 

EARTHQUAKE TOLERANCE:
Consider the earthquake acceleration and displacement that are necessary to cause the 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.

The primary sodium pool half fills a vertical cylinder 20 m diameter X 30 m high. Normally the sodium surface is horizontal. Consider a 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 space ceiling, which carries the gantry crane and monitoring system, is not structurally intended to withstand even sloshed liquid sodium. Hence an earthquake acceleration of greater than 1.5 g will almosst certainly result in a facility repair shutdown for an extended period.
 

SODIUM STRATIFICATION:
The thermal coefficient of expansion (TCE) of sodium is relatively large which implies that given an opportunity sodium will naturally thermally stratify. Hence when sodium is cooled by the intermediate heat exchange bundles the cool sodium tends to sink to the bottom of the sodium pool.-Hence, unless preventive measures are used, the temperature distribution in the liquid sodium will be one where the liquid sodium is coolest near the pool walls and along the pool bottom and is progressively warmer in the direction of the fuel assembly. Then the sodium that actually enters the bottom of the fuel assembly will get there via two routes. At full load about (2 / 3) of the circulating sodium flow volume will be warm ssodium because it circulates close to the fuel assembly. About (1 / 3) of the circulating sodium flow will be cold sodium because it is pushed up from the bottom of the sodium pool by cold sodium that flows down the inside of the pool walls.

For stable full power reactor operation we need the sodium temperature at the fuel assembly inlet to be constant independent of small changes in elevation of the stratification layer at the junction between the warm and cold sodium.

To achieve this objective without mechanical mixing the warm sodium must lose by thermal conduction the difference in temperature between the fuel assembly discharge and the fuel assembly inlet and the lost heat must raise the temperature of the sodium rising from the pool bottom by the difference in temperature between the fuel assembly inlet temperature and the pool bottom temperature.

The fuel assembly radius is about 7 m so its cross sectional area is about Pi (7 m)^2.

The maximum open area for sodium flow through the fuel assembly is about 52 m^2. About (2 / 3) of this flow becomes warm sodium and about (1 / 3) of this flow becomes cold sodium. Hence the maximum outside radius Rw of the flowing warm sodium is given by:
Pi(Rw)^2 - Pi (7 m)^2 = (2 / 3) 52 m^2
or
Rw^2 = [(2 / 3)52 m^2 + Pi (7 m)^2] / Pi
or
Rw = [(52 m^2 / Pi)(2 / 3) + (7 m)^2]^0.5
= [11.0347 m^2 + 49 m^2]^0.5
= 7.7482 m
which gives the radial width of the flowing warm sodium layer as:
Rw - 7 m = 0.7482 m

Outside the flowing warm sodium is cold sodium. To a first approximation the relevant cold sodium thickness is half of the warm sodium layer thickness or (.7482 m / 2) = .3741 m.

At the start of the circulating sodium flow path the difference in temperature between the warm sodium and the cold sodium is about 120 degrees C. Thermal conduction of heat will make this temperature difference diminish with time and flow distance.

The average thermal gradient is about:
[120 deg C / 0.5 m].

The area over which this thermal gradiant acts is about:
(2 Pi Rw)(6 m) + Pi(Rw)^2
= Pi Rw [12 m + Rw]
= Pi (7.7482 m)[12 m + 7.7482 m]
= 480.705 m^2

The thermal conductivity of liquid sodium is:
72.1 W / m-deg C

Hence the thermal power transferred by thermal conduction from the flowing warm sodium to the cold sodium is about:
[72.1 W / m deg C] X [120 deg C] X [480.705 m^2] X [1 / 0.5 m]
= 8.318 MWt

This calculated heat flow is two orders of magnitude too small. to fix this problem it is necessary to change the sodium flow pattern so that all the circulating sodium flows past the intermediate heat exchange bundles and the discharge temperature from these bundles is close to the desired fuel assembly inlet temperature.

This change will entail increasing the NaK flow through the intermediate heat exchange bundles so that the bundle temperature drop is less. ie Shunt part of the bundle discharge flow back to the bundle inlet to reduce the bundle temperature drop. That may mean increasing the bundle pipe size, the induction pump size and the bundle NaK flow cross sectional area.

This issue also complicates the natural NaK flow when the induction pump is not working.
 

This web page last updated October 31, 2024.

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