XYLENE POWER LTD.

FNR FUEL TUBES

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

INTRODUCTION:
This web page deals with FNR fuel tubes. The fuel tubes form a sealed barrier around the fuel rods that prevents intensely radioactive fuel and fission products mixing with the liquid sodium coolant and depositing on the cooler heat exchange and enclosure surfaces. Confinement of the fuel in fuel tubes also has the effect of confining the neutron flux to the proximity of the fuel assembly, which protects the intermediate heat exchanger and Na coolant tank from neutron excitation and/or cumulative neutron damage. Confinement of fuel and fission products also prevents these highly radioactive species contaminating the primary liquid sodium to the extent that intermediate heat exchange bundle replacement becomes difficult due to high radioactivity.

The dimensions and material properties of the FNR fuel tubes dictate many aspects of FNR design. The fuel tube material must operate at a high temperature, must be thermally conductive, must be suitable for tight dimensionally controlled fabrication, must have good welding characteristics, must have a small fast neutron absorption cross section and must have a low density BCC crystal lattice throughout its operating temperature range to minimize fast neutron induced fuel tube swelling.

The fuel tube material must also be chemically compatible with the fuel elements Pu, U, and Zr and the confined heat transfer element sodium, as well as the primary coolant sodium. The element zirconium preferentially binds with hot Pu to prevent formation of low melting point Pu-Fe eutectic.

The fuel tube material must tolerate material stress caused by contained core fuel swelling, by contained sodium thermal expansion / vaporization, by contained high pressure fission product inert gases and by the radial heat flux through the fuel tube walls.

The fuel tube must have a sufficient wall thickness to safely withstand repeated internal and external sodium liquid / solid phase transitions.

The fuel tube must have sufficient ID to allow the contained fuel to inject sufficient negative reactivity to balance positive reactivity injected by the sodium.

Another constraining issue is the maximum tolerable level of fuel tube material working stress during fuel bundle assembly, fuel bundle transport and prompt critical fuel disassembly.

When the fuel tube temperature is above the melting point of the contained bonding sodium the blanket fuel rods must be free to easily slide vertically by within the irradiated fuel tube. This free blanket rod sliding is essential both for normal thermal expansion and contraction, fuel disassembly under prompt critical conditions and is required for automated blanket rod mechanical sorting. An automated scan of the radiation emission from each recycled blanket fuel rod is required for minimizing chemical/electrolytic reprocessing of blanket fuel rods.
 

Each FNR has literally thousands of km of fuel tube. Hence the fuel tube material must be available from multiple suppliers at a competitive price. The issue of sourcing the fuel tube reduced the fuel tube material selection to either (3 / 8) inch OD or (1 / 2) inch OD. Calculations showed that (1 / 2) inch OD material resulted in too high a ratio of core fuel to reactor power. Hence the fuel tube material has to be (3 / 8) inch OD.

The main problem with the reduced fuel tube diameter is a reduction in sodium coolant flow gaps which can potentially lead to sodium flow blockage problems. Note that if (3 / 8) inch OD tube is used the fuel bundles may be too narrow for their length, so the fuel bundle structural design may have to be changed.

The fuel tube dimensions are in large measure constrained by the availability of suitable tubing which in turn is constrained by the process used to produce the fuel tube material. At the fuel tube ends the fuel tube ID should have an internal surface treatment to assist with making a perfect gas seal to the fuel tube end plugs.

An important issue in FNR design is realizing a reactivity versus temperature curve with a negative slope. The coolant sodium tends to make this slope more positive while plutonium alloy fuel tends to make this slope more negative. In order to maximize the ratio of plutonium alloy to coolant sodium the fuel tube ID should be as large as practical. Hence the fuel tube wall thickness should be as thin as practical. In 6 m lengths the smallest fuel tube wall thickness readily available is 0.035 inch to 0.036 inch. Hence this wall thickness was chosen.

In order to maximize the ratio of core fuel to coolant sodium most laboratory FNR designs use a hexagonal fuel tube layout. However, a problem with this hexagonal fuel tube layout is that over time the fuel tubes in the core zone tend to swell which significantly reduces the coolant sodium flow.

To avoid this potential sodium flow problem the fuel tubes are located on a square grid, which in the presence of fuel tube swelling allows a larger sodium flow. The fuel tube grid spacing is chosen to be (9 / 16) inch center to center. A consequence of this fuel tube spacing decision is that it may be necessary to maintain a substantial Pu fraction in the core fuel to ensure that the reactivity is sufficient.

In summary the fuel tubes are 0.375 inch OD, 0.036 inch wall, and are located on a (9 / 16) inch square grid.

A workable combination is (3 / 8) inch OD tube on a (9 / 16) inch rectangular grid with #14 = .0641 inch spacing wire wound on every fuel tube.
 

FUEL TUBE INSIDE DIAMETER CONTROL:
The initial fuel tube inside diameter must be tightly controlled. For each tube this ID is checked by pushing a ball bearing with a known diameter through a vertical fuel tube with a controlled air pressure. If the bearing becomes stuck in the tube the tube ID is too small. If the bearing fails to rise sufficiently due to air leakage past the bearing the tube ID is too large.
 

FUEL TUBE WALL THICKNESS:
The wall thickness of each fuel tube is checked by sliding an eddy current sensor through the tube. The readings from this sensor require that the fuel tube alloy be uniform. The wall thickness at the tube ends can be checked with a micrometer.

The minimum fuel tube wall thickness is set by:
a) Balancing the positive reactivity cused by the internal sodium;
b) The maximum pressure and hence hoop stress that the fuel tube must withstand. This pressure will be the vapor pressure of Cs and/or Na in a fuel overheat condition. In order to suppress prompt neutron criticality that vapor pressure must exceed the sum of the existing pressure in the fuel tube plenum plus the equivalent pressure imposed by gravity on the upper blanket rod stack.

In calculating the fuel tube wall thickness we must recognize that the thicker the fuel tube wall the less efficient the reactor will be at fuel breeding. However, if the fuel tube wall is too thin the operating life of the fuel bundle will be limited by the pressure rise inside the fuel tube plenum. Further, the fuel tube wall thickness cannot be too thin or on a rise in temperature the FNR negative reactivity injected by the fuel tube will not be sufficient to overcome the positive reactivity injected by the sodium internal to the fuel tube.

The transient yield stress of HT9 fuel tube material as a function of temperature is given by the paper: HT9 Cladding. At 600 degrees C this yield stress is about 600 MPa. If we assume a 3:1 safety factor the maximum design working stress is 200 MPa or 2000 atmospheres or 30,000 psi. However, we are concerned about steady creep which may further lower the working stress by another factor of three.

At a wall thickness of 0.036 inch the maximum working pressure rating Pmax of the fuel tube is given by:
2 (.036 inch) X 10,000 psi = Pmax X (0.375 inch - 2 (.036) inch)
or
Pmax = .072 inch X 10,000 psi / 0.303 inch
= 2376 psi

The maximum equivalent pressure imposed by gravity on the upper blanket rod stack is:
1.8 m X 16,000 kg / m^3 X 9.8 m / s^2 = 282.24 kPa

282.24 kPa X 14.7 psi / 101 kPa = 41.08 psi
 

FUEL TUBE DESCRIPTION:
Each fuel tube is 0.375 inch OD X 240 inch long. Note that:
240 inches X 0.0254 m / inch = 6.0906 m
The fuel tubes are supplied 240 inches +/- 1 inch long and should be cut to be exactly 6.001 m long.
 

FUEL TUBE ID = 0.303 inch +/-0.0005 inch

Optimum initial fissile fuel rod OD = 0.85 X 0.303 inch = 0.25755 inch = 6.542 mm
 

ACTIVE FUEL TUBES:
BOTTOM PLUGS
The bottom 2 X (5 / 8) inch = 0.03175 m of each movable fuel tube are occupied by the fuel tube bottom plug. The portion of this plug that is inside the fuel tube is slightly tapered for ease of insertion. Outside the fuel tube there is a shouder and then the bottom plug tapers to a blunt point about 0.1 inch in diameter. The plug is cooled in liquid N2, inserted, permitted to thermally expand and then is seal welded.

Above this plug is a 1.80 m high blanket rod stack. This stack consists of 6 X 0.30 m long X 7.0 mm diameter blanket fuel rods initially 90% uranium and 10% zirconium.

Then there are six 0.30 m long X 7.00 mm diameter blanket rods initially 90% uranium and 10% zirconium.

Then there is a plenum space:
(6.001 m - 2(0.03175 m) - 4.200 m = 1.7375 m
long which contains inert gases and reserve liquid sodium.

TOP PLUG
The top 2 (5 / 8) inch = 0.03175 m of the fuel tube are occupied by the fuel tube top plug.

The top plug has a (3 / 8 ) inch diameter shoulder followed by a top section with a (1 / 4) inch diameter course thread.

The maximum fuel tube length extension due to fast neutron induced fuel tube material swelling is anticipated to be:
(0.6 m) (0.125) = 0.075 m

However, it is anticipated that the fuel bundle steel components will swell almost equally to the fuel tubes, so the differential length expansion of the fuel tubes with respect to the fuel bundle steel frame will likely be negligible. The problem will be horizontal swelling for which there is a limited allowance.
 

PASSIVE FUEL TUBES:
The bottom 2 X (5 / 8) inch = 0.03175 m of each pasive fuel tube length are occupied by the fuel tube bottom plug.

Above the bottom plugs is a fuel rod stack consisting of:
14 X 0.30 m = 4.2 m X 7.0 mm diameter blanket fuel rods
initially 90% uranium and 10% zirconium.

The top 2 (5 / 8) inch = 0.03175 m of the passive fuel tube are occupied by the fuel tube top plug.

There is a remaining fuel tube plenum space:
(6.001 m - 2(0.03175 m) - 4.20 m = 1.7365 m
long which contains inert gases.
 

FUEL TUBE END PLUGS:
Each fuel tube has a top and bottom steel plug.

The fuel tube end plugs extend the overall length of a finished fuel tube assembly from 6.001 m to:
6.001 m + 4(5 / 8) inch = 6.001 m + 0.0635 m = 6.0645 m.

Outside the fuel tube is a (3 / 8) inch diameter retaining shoulder about (1 / 8 ) inch long. Then the bottom plug tapers to a blunt 0.1 inch ~ (1 / 8) inch diameter blunt point which rests on a support grating intersection.

The top plug has an external (1 / 4) inch thread that allows seleective fuel tube lifting.

Each fuel bottom bottom plug is made of 0.375 inch OD round steel rod 6.35 cm long. The upper 2(5 / 8) inch of the fuel tube bottom plug length is machined down to 0.303 inch diameter with a short taper to assist with insertion in the fuel tube. The plug has a 1 / 8 inch long shoulder to prevent over insertion. The bottom (9 / 8) inch of this plug tapers almost to a blunt point that is supported by a (1 / 8) inch___ thick X (1 / 8)____ inch thick grating plate intersection. Thus the fuel tube bottom plug supports the bottom of the fuel tube (10 / 8) inch above the top of the grating. Immediately prior to insertion in the fuel tube the fuel tube bottom plug is cooled with liquid nitrogen so that when it warms up it will expand to make a tight joint with the fuel tube. Then the fuel tube bottom plug is seal welded to the fuel tube.

Each fuel tube top plug is made of (3 / 8) = 0.375 inch diameter round steel rod:
4 X (5 / 8) inch = (20 / 8 inch) long.
The bottom 2 (5 / 8) inch of the fuel tube top plug is machined down to 0.303 inch OD to fit inside the fuel tube. There is a taper to improve insertion. Immediately above the machined lower section is a
2 (1 / 8) inch length of unmachined shoulder section that prevents over insertion in the fuel tube. The remaining
2(5 / 8) inch - 2(1 / 8) inch = 1.0 inch of top end plug has an external (3 / 8) inch coarse thread. The top of this thread is slightly tapered to permit easy starting of am internally threaded lifting tool. Immediately prior to insertion in the fuel tube the fuel tube top plug is cooled with liquid nitrogen so that when it warms up it will expand to make a tight joint with the fuel tube. Then the fuel tube top plug is seal welded to the fuel tube.
 

ASSEMBLY OF FUEL TUBES:
A key issue with the fuel tube fabrication is precise control of the fuel tube ID (inside diameter). This ID control must be comparable to the ID control of a rifle barrel so as to ensure safe, reliable and rapid fuel disassembly in the event of a prompt neutron critical condition.

The first step in fuel tube assembly is to check the fuel tube ID.

The next step is to use an eddy current tester to confirm the thickness and uniformity of the fuel tube wall.

Then the fuel tube inside ends must be mechanically and chemically cleaned in a nitrogen atmosphere.

Every second fuel tube is spiral wound on the outside with 0.12 inch OD______ stranded chrome steel wire which is spot welded in place and serves to maintain the desired inter fuel tube spacing. The spiral turn to turn distance is about 0.5 m to laterally stabilize the fuel tubes every half metre while minimizing the liquid sodium coolant flow resistance.

The next step in fuel tube assembly is application of the top plug. This is done at room temperature with the tube in its normal upright position. The top plug is cooled in liquid N2 and while cold is inserted into the top tube end which is at room temperature. As the top plug warms it thermally expands to make a tight seal. Then the top plug is electric seal welded in place. The seal might be enhanced by use of a high melting point solder coating on both the end plug and the end of the fuel tube.

The fuel tube is then slipped into a (3 / 4) inch ID pipe filled with He. A vacuum pump and He tuned mass spectrometer are connected to the open end of the fuel tube and the top plug seal and fuel tube walls are leak tested.

After the top plug seal and fuel tube walls have been proven to be good the fuel tube is inverted and heated to about 120 degrees C in a nitrogen atmosphere. The fuel rods are dropped into the fuel tube along with a measured quantity of liquid sodium. A liquid N2 cooled bottom plug is then applied, permitted to warm to room temperature and then electric welded in place. Note that the precise angular orientation of the bottom plug with respect to the top plug around the fuel tube axis is important. While the tube is still at 120 degrees C it is returned to an upright position. This orientation change causes the fuel rods to slide to their intended final positions.

The assembled fuel tube is cooled to room temperature so that the internal liquid sodium solidifies, holding the fuel rods in place at their desired final positions. Then the balance point of the fuel tube is checked to ensure that there is no internal fuel rod jam.

Note that the seal of the fuel tube top plug, which contains inert gas at ~ 460 C, is more critical than the seal of the bottom plug, which contains liquid sodium at 340 C. Hence the top plug is applied first and its seal is tested with a helium leak detector before the fuel tube is assembled upside down and the bottom plug applied. Then, while the sodium inside the fuel tube is still liquid, the fuel tube is returned to its normal upright position for storage. Its balance point must be tested to confirm that the fuel rods are all stacked at the bottom, not stuck somewhere else inside the fuel tube. A simple balance point tester is a horizontal (3 / 4) inch ID pipe about 10 feet long. The fuel tube is slid through this 1 inch ID pipe until the fuel tube projects out from one end of the (3 / 4) inch ID pipe by about 10 feet. At its exact balance point it will tip inside the horizontal (3 / 4) inch ID pipe.
 

FUEL TUBE LIFTING TOOL:
An individual fuel tube lifting tool has an (1 / 2) inch OD end and a (1 / 4) inch internal coarse thread. A fuel tube lifting tool is screwed onto the top plug of an assembled fuel tube prior to selective lifting of the assembled fuel tube. Extraction of the lifting tool relies on inter tube winding friction to prevent undesired tube rotation.
 

FUEL TUBE MATERIAL SELECTION:
With respect to the FNR design developed on this web site natural circulation of the liquid sodium is used to achieve mechanical simplicity. At full load the temperature at the bottom of the fuel asembly is about 400 degrees C and the temperature at the top of the liquid sodium pool is about 460 degrees C. Various parts of a fuel tube normally operate in the temperature range 400 C to 510 C. In the case of two adjacent sodium cooling channels being blocked the fuel centerline temperature can rise to 560 degrees C.

It is shown on the web page FNR FUEL TUBE WEAR that to minimize fuel tube material swelling historically a good fuel tube material was the alloy HT-9. HT-9 initially contains 12% chromium in iron which keeps HT-9 in the alpha phase with a BCC lattice. The chromium also has a BCC lattice. HT-9 contains almost no nickel.

In the temperature range 340 deg C to 470 deg C HT-9 is subject to fast neutron induced embrittlement. This enbrittlement is in part due to the presence of nickel, the fraction of which must be minimized.

Theoretically the problem with Ni is that on neutron activation Ni-58 forms the long lived isotope Ni-59. Ni-59 has a large neutron capture cross section. Ni-60 alpha decays leaving He-4 atoms in the metal lattice that accumulate at grain boundaries and cause enbrittlement. Hence the fuel tube alloy should have the lowest possible nickel fraction.

Nickel has been successfully used for many years as a major component of stainless steel and other high working temperature alloys such as Inconel-600. However, as compared to iron and chromium nickel has an unfavorable crystal lattice and has larger fast neutron absorption and scattering cross sections.

Another practical consideration in choosing fuel tube material is its weldability. Each FNR fuel tube assembly has ~ 450,000 _______fuel tubes that must be automatically fabricated, assembled, and tested.

During a fuel cycle due to fast neutron irradiation the fuel tube metal significantly changes its physical properties including its: thermal conductivity TC, thermal coefficient of expansion TCE, Young's Modulus Y and yield stress Sy. Also, as the fuel tube ages its contained internal inert gas pressure rises.

If the fuel tube alloy composition is not correct a complicating issue is a phase change out of BCC within the fuel tube operating temperature range. Such a phase change in a fast neutron flux will cause material swelling. In a practical FNR the bottom 1.825 m of fuel tube operates in the temperature range 340 deg C to 400 degrees C, the top 3.775 m of fuel tube operates at about 460 deg C and there is a middle transition region about 0.40 m high where the temperature transition from 400 deg C to 460 deg C occurs.

If the alloy composition is correct the fuel tube maintains a low density BCC crystal lattice through its operating temperature range which minimizes material swelling caused by the fast neutron flux. However, after prolonged exposure to the fast neutron flux this material becomes quite brittle. This brittleness can be relieved by operating the reactor at a low power to raise the entire sodium pool temperature sufficiently to anneal the fuel tubes.

A problem with HT-9 fuel tubes is that Pu in the fuel and Fe in the fuel tube tend to merge to form a low melting point eutectic. This issue can be mitigated sufficiently for < 500 degree C operation by adding 10% Zr to the fuel rod alloy. However, only a fraction of the Zr goes into metal alloy solution. To realize significantly higher temperature operation a different fuel tube metal alloy is likely required.

Significant problems with HT-9 are poor thermal conductivity, neutron absorption and and loss of strength at high temperatures.

A good reference with respect to neutron absorption is:
Neutron Capture Cross Sections.
 

FUEL TUBE ALLOY HT-9:
The alloy currently under consideration for FNR fuel tubes is HT-9. HT-9 is a Fe-Cr alloy with low carbon, low nickel and relatively low chromium content.
 

HT-9 is a Martensitic Steel Alloy described by Chen as consisting of the weight percentages:
Fe + 12% Cr + 1% Mo + 0.5% W + 0.5% Ni + 0.25% V + 0.2% C
and described by Leibowitz and Blomquist as consisting of the weight percentages:
85.3% Fe + 12% Cr + 1.0% Mo + 0.5 % W + 0.5% Ni + 0.5% V + 0.2% C

As compared to other potential fuel tube materials HT-9 is unique in its low Ni fraction.

The big advantage of HT-9 is minimal material swelling at high fast neutron exposures. Even with HT-9 an increase in tube diameter of 3.5% was observed at a neutron fluence of 31.4 X 10^22 neutrons / cm^2 at a temperature of 420 C. HT-9 is claimed to exhibit half the creep of other tube materials.

A disadvantage of HT-9 is that when fast neutron irradiated HT-9 is operated below 425 degrees C it becomes extremely brittle.
 

BRASS BALL BEARINGS:
The blanket rod stacks have brass ball bearings between the rods that have a precise 0.300 inch OD at working temperature. The purpose of these balls is to make the fuel rods above the balls behave like blowgun projectiles while inside the fuel tubes. Ideally at room temperature the balls should easily slide inside the fuel tubes with an almost airtight fit. The nominal fuel tube ID is 0.303 inches. In a prompt neutron critical condition liquid sodium in contact with the hot core fuel rod will vaporize. The confined high pressure sodium vapor should propel the adjacent liquid sodium and hence the fuel rods above the brass balls into their corresponding fuel tube plenums causing safe temporary disassembly of the core fuel.

Note that the in a prompt neutron critical condition the Na adjacent to the core fuel rod will vaporize. The plenum must be large enough to briefly accommodate this vapor.
 

THERMAL FLUX:
At the contemplated thermal flux the temperature drop across a 0.036 inch thick fuel tube wall is ~ 10 deg C.
 

The maximum height Hb of blanket rod that one atmosphere can support by is given by:
Hb = 0.760 m X (density of mercury) / (density of blanket rod)
= 0.760 m X (13472 kg / m^3) / (15,884 kg / m^3)
= 0.6446 m

Hence the core fuel rod is chosen to be 0.60 m long X 6.54 mm diameter.

Thus the presure necessary to lift the upper blanket rod stack is:
(1.8 m / 0.6446 m) X 14.7 psi = 41.05 psi

This pressure in combination with the plenum volume limits the maximum amount of inert gas fission products permitted inside the fuel tube, which limits the maximum fuel burnup per fuel cycle.
 

FUEL TUBE PLENUM:
The internal pressure stress on the fuel tube walls is limited by provision of a gas plenum for each fuel tube. Above the top blanket rod is a 1.75 m high plenum. The plenum has sufficient volume to store at a reasonable pressure the inert gas fission products that accumulate during one fuel cycle.

This plenum also stores liquid sodium to accommodate core zone fuel tube swelling and to permit differential sodium, fuel and fuel tube material thermal expansions.

CHECK THE SUFFICIENCY OF THE PLENUM VOLUME UNDER PROMPT NEUTRON CRITICAL CONDITIONS THAT VAPORIZE THE Na ADJACENT TO THE CORE FUEL ROD.
 

FUEL BONDING SODIUM:
There is sufficient liquid sodium inside each fuel tube to always provide good thermal contact between the fuel rods and the inside wall of the fuel tube and to chemically absorb the corrosive fission products bromine and iodine. Note that the sodium top level changes over time to accommodate fuel tube material swelling. Towards the end of the fuel tube life spare sodium drains down from the fuel tube plenum into the swollen portion of the fuel tube, increasing the plenum volume available for inert gas storage.
 

LATERAL TORQUE:
In a reactor fuel bundle the fuel tubes are supported by their ends. However, absent some additional support, other than adjacent fuel tubes which share the same problem, purely end support of fuel tubes will lead to excessive material stress, especially during road transport when the tubes are nearly horizontal, but the whole is subject to road bumps. To grasp the importance of this issue consider a round tube that is horizontally fixed at one end but is acted on by gravity along its length which creates a torque Tor.

The fuel tube is cylindrical with an internal radius Ri and and external radius Ro. Measured from the fuel tube center line the strain in the fuel tube material is proportional the the height H above the center line:
Strain = K H
where K is an applied torque dependent amount yet to be determined.

In the material elastic region strain is related to stress by:
Y = (stress / strain)
where Y is a material constant for the fuel tube.

The radial thickness of the fuel tube wall is (Ro - Ri)

Define:
Theta = angle measured about the axis of the horizontal fuel tube.

An element of fuel tube cross sectional area is:
[(Ri + Ro) / 2] dTheta [Ro - Ri]

An element of total torque T related to 4 such elements of area around the tube is:
dTor = 4 [(Ri + Ro) / 2] dTheta [Ro - Ri] [stress] [(Ro + Ri) / 2][sin(Theta)]

Recall that in the material elastic region:
stress = Y [strain]
= Y K H
= Y K [(Ro + Ri) / 2] sin(Theta)

Note that stress is maximum at Theta = (Pi / 2) radians.

Let Sy = yield stress
Then when stress = Sy:
Sy = Y K [(Ro + Ri) / 2]

Assume that a safe working stress is (Sy / 3). Then the maximum safe working value of K = Kw is given by:
(Sy / 3) = Y Kw [(Ro + Ri) / 2]
or
Kw = (2 Sy) / [3 Y (Ro + Ri)]

Hence an element of total torque Tor is:
dTor = 4 [(Ri + Ro) / 2] dTheta [Ro - Ri] [(Ro + Ri) / 2][sin(Theta)]Y K [(Ro + Ri) / 2] sin(Theta)
 
= 4 [(Ri + Ro) / 2]^3 dTheta [Ro - Ri] [sin(Theta)]^2 Y K

Hence the total torque Tor is given by:
Tor = Integral from Theta = 0 to Theta = (Pi / 2) of:
4 [(Ri + Ro) / 2]^3 dTheta [Ro - Ri] [sin(Theta)]^2 Y K
 
= 4 [(Ri + Ro) / 2]^3 [Ro - Ri] [sin(Theta)]^3 Y K / 3|Theta = (Pi / 2)
- 4 [(Ri + Ro) / 2]^3 [Ro - Ri] [sin(Theta)]^3 Y K / 3|Theta = 0
 
= 4 [(Ri + Ro) / 2]^3 [Ro - Ri] Y K / 3

Thus in the material's elastic region the total torque Tor is given by:
Tor = 4 [(Ri + Ro) / 2]^3 [Ro - Ri] Y K / 3

Recall that the maximum working value of K = Kw is given by:
Kw = (2 Sy) / [3 Y (Ro + Ri)]
which gives the maximum working torque Torw as:
Torw = 4 [(Ri + Ro) / 2]^3 [Ro - Ri] Y Kw / 3
= {4 [(Ri + Ro) / 2]^3 [Ro - Ri] Y / 3} {(2 Sy) / [3 Y (Ro + Ri)]}
= {[(Ri + Ro)^2] [Ro - Ri]} {Sy / 9}

Thus we have derived the very important fuel tube design equation:
Torw = {[(Ri + Ro)^2] [Ro - Ri]} {Sy / 9}

Try the practical values:
Ro = 0.1875 inch
Ri = 0.1515 inch
Sy = 30,000 lb / inch^2

Then:
Tw = {[(Ri + Ro)^2] [Ro - Ri]} {Sy / 9}
= {[(.339 inch)^2] [0.036 inch]} {30,000 lb / 9 inch^2}
= 13.79 lb - inch

This lateral torque limit sets the maximum distance between adjacent fuel tube stabilization points and constrains fuel bundle design, handling, transportation and earthquake protection. A thicker wall tube is not a solution because it increases the ratio of steel to fuel which reduces fuel breeding.

In general all the fuel tubes must be supported or stabilized all along their lengths. This issue is particularly important for road transport. This requirement imposes size and strength requirements on the fuel bundle windings, fuel bundle corner girders, fuel bundle shroud sheets, fuel bundle diagonal plates and the open steel lattice that indirectly support and stabilize the fuel tubes. The wire winding around the tubes must have sufficient turns per unit length and must be sufficiently snug to provide the required lateral stabilization. In order to minimize the steel to fuel ratio it is necessary to assume that during normal handling the maximum horizontal accelertaion to which the fuel bundle will be exposed is about (1 / 2) g.

A related issue is protecting the fuel tubes from horizontal acceleration induced by an earthquake.

In operation the entire fuel assembly and open steel lattice rests on a layer of ball bearings which isolate it from major earthquake caused horizontal accelerations of up to 3 g____ at a frequency of ____ Hz.
 

HEAT SOURCE LOCATION:
The purpose of the reactor is to supply the required nuclear heat. The depth of the liquid sodium in the liquid sodium pool is 15.0 m. The heat is emitted by the reactor core zone, which is situated betwen 4.8 m to 5.2 m above the bottom of the liquid sodium pool.
 

ASSEMBLED FUEL TUBE MASS:
Each active fuel tube contains 1 X 0.60 m long core rod and 12 X 0.30 m blanket rods.

Mass of fuel rods per active fuel tube :
(0.3226 kg / core rod) + 12 (0.18292 kg / blanket rod)
= 2.51764 kg / fuel tube.

Fuel Tube Steel:
Mass = Pi [(0.375 inch)^2 - (0.303 inch)^2] / 4 X 6.0 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3
= 1.1686 kg

2 Fuel Tube End Plugs:
Mass = 2 X Pi X (.375 inch / 2)^2 X 2.5 inch X (.0254 m / inch)^3 X 7.874 X 10^3 kg / m^3
= 0.07125 kg

Sodium:
Each fuel tube contains sufficient liquid sodium to cover the core and blanket rods up to a height of 4.0 m.
 

The volume of liquid sodium initially required inside a fuel tube is:
Pi [(.303 inch / 2)^2] [0.0254 m / inch]^2 [4.2 m] - Pi[((6.54 / 2) X 10^-3 m)^2 (0.6 m)] - Pi [((7.0 / 2) X 10^-3 m)^2 (12)(0.30 m)]
= Pi [0.62193 X 10^-4 m^3 - 0.064157 X 10^-4 m^3 - 0.441 X 10^-4 m^3]
= 0.3668 X 10^-4 m^3

The mass of this sodium is:
0.3668 X 10^-4 m^3 X 927 kg / m^3 = 0.0340 kg
 

TOTAL MASS OF ONE ACTIVE FUEL TUBE:
For each fuel tube:
Fuel Rods + tube steel + end plug steel + sodium
2.51764 kg + 1.1686 kg + 0.07125 kg + 0.0340 kg = 3.7915 kg / active fuel tube
 

FUEL DETAIL:
In each fuel tube the FNR top and bottom blanket fuel rod stacks are each:
6(.30 m) + (.60 m) + 6(.30 m) = 4.2 m long.
This blanket rod configuration allows a small amount of fuel tube bending. Even so these blanket rods still must be straight to within +/- 0.4 mm over each 0.30 m length. The individual blanket rods are made shorter than the individual core rods to ensure easy sliding, to allow easy fuel rod mechanical sorting and to prevent accidents resulting from fuel rod type mix ups.

The FNR core fuel rods are initially 0.60 m long but over time may swell to average lengths of 0.7 m long. This core rod length achieves the desired core zone reactivity and allows a small amount of fuel tube bending.

Each active fuel tube contains 12 X 0.30 m long X 7.0 mm diameter beaded blanket rods initially consisting of 90% uranium and 10% zirconium and 1 X 0.60 m long X 6.54 mm diameter beaded core rods initially consisting of 70% uranium-20% plutonium-actinide-10% zirconium alloy.

Each passive fuel tube contains 14 X 0.30 m long X 7.0 mm diameter blanket rods initially consisting of 90% uranium and 10% zirconium.
 

HOOP STRESS:
The material hoop stress Sh in a simple tube with inside radius Ri, outside radius Ro, pressure differential DeltaP is given by:
(DeltaP) (2 Ri) = 2 (Ro - Ri) Sh
or
(DeltaP) = [(Ro - Ri) / Ri] Sh

Note that the hoop stress is tensile and is approximately evenly distributed through the tube material.

Choose the maximum value of Sh to be:
10,000 psi = 68.7 MPa.
This is the allowable working material hoop stress with no thermal stress.

Then the corresponding internal pressure in the tube is:
DeltaP = [(Ro - Ri) / Ri] Sh
= [(0.036 inch) / (0.1515 inch)] 68.7 MPa
= 16.32 MPa
This is the maximum allowable gas working pressure inside the tube with no wall thermal stress.
 

If the inside surface of the tube is hot at temperature Ti and if the outside surface of the tube is cold at temperature To the hot side is under compression and the cold side is under tension:
Hot side strain = - [2 Pi Ri (TCE) (Ti - Ta)] / [2 Pi Ri]
= - (TCE) (Ti - Ta)] and
Cold side strain = [2 Pi Ro (TCE) (Ta - To)] / [2 Pi Ro]
= [(TCE) (Ta - To)]
where:
TCE = temperature coefficient of expansion
Ti = inside wall temperature
To = outside wall temperature
Ta = average wall temperature
= (Ti + To) / 2.

Young's Modulus Y is defined by:
Y = (stress) / (strain)

Hence cold side thermal stress Stc is given by:
Stc = Y (cold side strain)
= Y [(TCE) (Ta - To)]
= Y [(TCE) [((Ti + To) / 2) - (To)]
= Y [(TCE) [(Ti - To) / 2]

The total tensile stress on the outside surface of the fuel tube material is:
(Sh + Stc) = [(DeltaP) Ri / (Ro - Ri)] + [Y (TCE) (Ti - To) / 2]
which must be less than the rated working stress 68.7 MPa.
 

MATERIAL PROPERTIES:
Define:
TC = thermal conductivity
TCE = thermal coefficient of expansion
DeltaT = (Ti - To) = temperature drop across steel tube wall
Y = (stress / strain) = Young's modulus
Sy = yield stress

Key material properties are set out in the following table:

PROPERTY	316L	HT-9	Fe	Cr
Rho	7966 kg / m^3		7.874 kg / m^3
TC @ 25 C	15 W / m-K	26.2 W / m-K	80.4 W / m-K	93.9 W / m-K
TC @ 500 C	15 W / m-K	26.2 W / m-K
TCE @ 25 C	18 X 10^-6 / K	15 X 10^-6 / K	11.8 X 10^-6 / K	4.9 X 10^-6 / K
TCE @ 500 C	18 X 10^-6 / K	15 X 10^-6 / K		4.9 X 10^-6 / K
Y @ 25 C, no rad.	-	2000 GPa?	211 GPa	279 GPa
Y @ 250 C, no rad.	-	2000 GPa?
Y @ 250 C, with rad.		2000 GPa?
Bulk Y @ 500 C	120 GPa
Sy @ 25 C, no rad.	291.3 MPa	-	400 MPa
Sy @ 250 C, no rad.		600 MPa		200 MPa
Sy @ 250 C, rad		900 MPa
Sy @ 400 C, rad		600 MPa to 900 MPa
Sy @ 500 C, no rad	167 MPa	400 MPa to 550 MPa
Sy @ 500 C, with rad		450 MPa to 600 MPa

 

SOLID SODIUM INSIDE FUEL TUBE:
As shown at FNR Design in order to withstand local melting of an annulus of sodium around a fuel rod the sodium inside the fuel tube the fuel tube wall thickness should be about 0.035 inch for a 0.500 inch OD HT-9 fuel tube.
 

THERMAL WALL STRESS:
Recall that:
(Sh + Stc) = [(DeltaP) Ri / (Ro - Ri)] + [Y (TCE) (Ti - To) / 2]
which must be less than the rated working stress 68.7 MPa.

For a HT9 fuel tube:
Y = 120 GPa?_______
TCE = 15 X 10^-6 / deg C
(Ti - To) / 2 = 4 deg C

Hence:
[Y (TCE) (Ti - To) / 2] = 120 GPa X 15 X 10^-6 X 4.0
= 120 X 10^3 MPa X 15 X 10^-6 X 4.0
= 120 X 15 X 10^-3 X 4.0 MPa
= 7.2 MPa

Thus:
[(DeltaP) Ri / (Ro - Ri)] + [Y (TCE) (Ti - To) / 2] < 68.7 MPa
implies that:
[(DeltaP) Ri / (Ro - Ri)] < 68.7 MPa - 7.2 MPa = 61.5 MPa

Ri / (Ro - Ri) = 0.215 inch / 0.035 inch
= 6.14

Hence:
DeltaP < 61.5 MPa / 6.14
or
DeltaP < 10.016 MPa
This gas pressure in the fuel tube plenum is caused by fission products that are gaseous at 511 degrees C.
 

FISSION PRODUCT ANALYSIS:
The following data relies on a fission product mass distribution calculated by Peter Ottensmeyer using ENDF Brookhaven data files.

Atomic Number	Symbol	MASS % of fission products	MP	BP	GAS at 500 C?
31	Ga	0.038	29.78 C	2403 C	N
32	Ge	0.328	937.4 C	2830 C	N
33	As	0.526	__	613 C	?
34	Se	2.002	217 C	685 C	?
35	Br	2.092	- 7.2 C	58.78 C	Y
36	Kr	5.746	- 156.6 C	- 152.3 C	Y
37	Rb	4.428	38.89 C	686 C	?
38	Sr	9.307	769 C	1384 C	N
39	Y	4.587	819 C	1194 C	N
40	Zr	10.946	1852 C	4377 C	N
41	Nb	3.862	1024 C	3027 C	N
42	Mo	3.785	2610 C	5560 C	N
43	Tc	0.494	2157 C	4265 C	N
44	Ru	0.246	38.89	686	?
45	Rh	0.048	1966 C	3727 C	N
46	Pd	0.077	1554 C	2970 C	N
47	Ag	0.042	962 C	2212 C	N
48	Cd	0.208	320.9 C	765 C	N
49	In	0.381	156.6 C	2080 C	N
50	Sn	4.191	231.88 C	2260 C	N
51	Sb	3.848	630.74 C	1750 C	N
52	Te	7.667	452 C	1390 C	N
53	I	4.657	113.5 C	184.35 C	Y
54	Xe	8.799	- 111.9 C	- 107.1 C	Y
55	Cs	4.294	28.40 C	669.3 C	?
56	Ba	6.409	725 C	1640 C	N
57	La	1.886	921 C	3457 C	N
58	Ce	2.195	799 C	3426 C	N
59	Pr	0.431	931 C	3512 C	N
60	Nd	0.438	1024 C	3027 C	N
61	Pm	0.041
62	Sm	0.011	1077 C	1791 C	N
63	Eu	0.001	822 C	1597 C	N
64	Gd	0.000	1313 C	3266 C	N
65	Tb	0.000	1360 C	3123 C	N
66	Dy	0.000	1412 C	2562 C	N

Thus up to 600 degrees C the fraction of fission products that are gas is:
2.092% + 5.746% + 4.657% + 8.799% = 21.294%

On the above table we must be concerned about anything that has a melting point between 300 C and 511 C because if such materials leak into the primary liquid sodium they will deposit on the cool heat exchange surfaces. The main concerns are Cd which will deposit on any surface below 320 C and Te which will deposit on any surface below 452 C.

The bromine and iodine will chemically react with the liquid sodium inside the fuel tube producing high melting point solids. Hence, up to 600 degrees C the remaining fission products that are gas are just Kr and Xe and the percent of fission products that are gas is:
5.746% + 8.799% = 14.545%

In the temperature range 600 C to 700 C other fission products start to contribute to the plenum pressure to a maximum of:
0.526% + 2.002% + 4.428% + 0.246% + 4.294% = 9.494%

Note that to allow operation in this temperature range at the same pressure the plenum volume must be substantially increased.
 

Core rod mass = (0.3226 kg)

Let Fb = fuel burnup fraction in one fuel cycle ~ 0.15

Core rod mass converted to fission products in one fuel cycle is:
Fb (0.3226 kg)(.14545)
= 0.15 (0.3226 Kg)(0.14545)
= 0.00704 kg
= 7.04 g
 

MINIMUM PLENUM LENGTH REQUIRED FOR INERT GAS STORAGE:
From the above table the weight of krypton produced in one fuel tube in one fuel cycle is:
Fb (0.3226 kg) X 5.746 X 10^-2

The atomic weight of krypton is: 83.798

The number of moles of krypton produced is:
[Fb (0.3226 kg) (5.746 X 10^-2) X 1000g / kg] / [83.798 g / mole]

From the above table the weight of xenon produced in one fuel tube in a single fuel cycle is:
Fb (0.3226 kg) (8.799 X 10^-2)

The atomic weight of xenon is: 131.293

The number of moles of xenon produced is:
[Fb (0.3226 kg) (8.799 X 10^-2) X 1000 g / kg] / [131.293 g / mole]

The total number of moles of krypton and xenon gas produced in one fuel cycle is:
[ Fb (0.3226 kg) (5.746 X 10^-2) X 1000g / kg] / [83.798 g / mole]
+ [Fb (0.3226 kg) (8.799 X 10^-2) X 1000 g / kg] / [131.293 g / mole]
= [Fb (0.3226) [(57.46 / 83.798) + (87.99 / 131.293)] moles
= [Fb (0.3226) [(0.6857) + (0.6702)] moles
= 0.43741 Fb moles inert gas

From physical chemistry, 1.000 mole of an inert gas at 273 deg K and 0.101 MPa has a volume of 22.4 X 10^-3 m^3. That 1.000 mole of inert gas at 511 deg C = 784 deg K and at the above calculated maximum pressure of 16.32 MPa occupies a volume of:
(22.4 X 10^-3 m^3 / mole) X (784 K / 273 K) X (0.101 MPa / 16.32 MPa)
= 0.3981 X 10^-3 m^3 / mole

Hence the plenum volume required for storage of inert gas fission products at 511 C and 16.32 MPa is:
(0.3981 X 10^-3 m^3 / mole) X (0.43741 Fb) moles inert gas)
= (0.174 Fb) X 10^-3 m^3

The inside cross sectional area of the fuel tube is given by:
Pi (0.303 inch / 2)^2 X (.0254 m / inch)^2
= 0.4652 X 10^-4 m^2

Hence the minimum dedicated plenum length required for inert gas storage is:
[(0.174 Fb) X 10^-3 m^3] / 0.4652 X 10^-4 m^2]
= 3.74 Fb m

For Fb = 0.15 the dedicated plenum length required for inert gas storage is:
3.74 Fb m = .561 m
which is consistent with the 1.6 m of available plenum height in the fuel tubes.

The dedicated gas portion of the plenum sets the internal pressure in the fuel tube as the fuel rods release inert gas fission products.
 

PLENUM VOLUME REQUIRED TO ACCOMMODATE EXTRA LIQUID SODIUM:
Each fuel tube contains sufficient liquid sodium to cover the core and blanket rods up to a height of 4.3 m to ensure good thermal contact between the rods and the enclosing steel tube.

Each fuel tube has a plenum to provide volume for inert gas storage, for liquid sodium storage and to provide allowance for fuel tube swelling and differential liquid sodium thermal expansion.

The potential increase in fuel tube internal volume due to fuel tube swelling around the core rods is:
Pi{ [(1.15 X .303 inch) / 2)^2 - [(.303 inch)/ 2]^2} X 0.7 m X (.0254 m / inch)^2
= Pi{[.030354 - .02295] inch^2} X 0.7 m X (.0254 m / inch)^2
= 1.0504 X 10^-5 m^3

The fuel tube inside cross sectional area is:
Pi (.303 / 2)^2 inch^2 X (.0254 m / inch)^2
= 4.652 X 10^-5 m^2

The length of plenum required for this extra liquid sodium is:
1.0504 X 10^-5 m^3 / 4.652 X 10^-5 m^2
= 0.2257 m
 

TOTAL PLENUM REQUIREMENT:
Hence the minimum total plenum height is:
(inert gas height) + (sodium height due to fuel tube swelling)
= 0.561 m + 0.2257 m
= 0.79 m

The available plenum height is certain to be at least:
1.8 m - 0.064 m = 1.73 m
which is sufficient to ensure that the plenum gas pressure will not be a constraining issue for the contemplated FNR. The burnup fraction will likely be limited by depletion of Pu and by accumulation of neutron absorbing fission products. Another reason for having a tall fuel tube plenum is to enhance natural circulation of liquid sodium via the chimney effect.
 

FUEL DISASSEMBLY:
For old fuel disassembly will start at about 700 degrees C due to vaporization of the fission product Cs.

New fuel will disassemble due to the sodium vapor pressure if the core fuel gets very hot as in a prompt neutron critical condition.<

TEMPERATURE DEG C	Na VAPOR PRESSURE IN ATMOSPHERES
1047	3.78
1175	8.34
1232	11.20
1399	25.50
1468	33.30
1522	41.27

The melting point of iron is 1538 deg C

The melting point of chromium is 1907 deg C

Note that as the core fuel temperature rises from about 1000 degrees C to 1200 degrees C the sodium vapor pressure will disassemble the fuel in the core zone driving the core rods of the fixed fuel bundles into the fuel tube plenums. This fuel disassembly will occur at least 300 degrees C below the melting point of chromium steel fuel tubes.
 

OTHER FUEL TUBE MATERIAL CONCERNS:
Issues that need to be clarified are:
1) Is there a change in fuel tube Youngs Modulus with temperature and neutron irradiation?
and
2) Is there a change in fuel tube wall thermal conductivity with temperature and neutron irradiation?
 

REACTOR THERMAL FLUX:
Assume a 10 deg C temperature drop across the fuel tube wall. Thus the maximum safe continuous operating heat flux through the HT-9 steel tubes of the reactor core is:
10.0 deg C X 26.2 W / m-deg C / (.036 inch X .0254 m / inch) = 286,526 W / m^2

To realize the rated reactor power each active fuel tube must conduct:
1,000,000 kWt / 299,776 active fuel tubes = 3.336 kWt / active fuel tube

Hence the required minimum active core fuel rod length L is given by:
3336 Wt / [L (.375 inch X Pi X .0254 m / inch)} = 286,526 Wt /m^2
or
L = 3336 Wt / [(.375 inch X Pi X .0254 m / inch) X 286,526 Wt / m^2]
= 0.389 m

Thus we need to choose the initial Pu concentration in the fuel rods such that the reactor is critical when the movable and fixed core fuel rods overlap by about 0.389 m. As the Pu concentration gradually decreases this overlap must increase.

Note that this thermal power limit is dependent on the thickness of the middle core zone. At relatively low Pu concentrations the core zone may be as thick as 0.60 m whereas at high Pu concentrations the core zone thickness might be 0.389 m. The actual core zone thickness will be indicated by the amount of projection of the indicator tubes above the primary sodium surface. The amount of heat that can actually be carried away may be limited by the liquid sodium chimney effect.
 

POSSIBLE FUTURE ALTERNATIVE FUEL TUBE MATERIAL:
A possible future fuel tube material presently under consideration is a combination of the Mo isotopes Mo-92 and Mo-94. One of the Mo isotopes, Mo-95, has a high neuron absorption cross section. Hence ideally the Mo used for fuel tube fabrication should be highly depleted in Mo-95.

Molybdenum has the necessary high melting point, high temperature strength and BCC crystal lattice.

However, to obtain a low average neutron absorption cross section it is necessary to do an isotope separation which highly rejects Mo-95 from the fuel tube material. On purely theoretical grounds it is thought that a liquid sodium cooled FNR with Mo-92, 94 fuel tubes could operate at coolant temperatures up to 800 degrees C. Another challenge with Mo is development of a process for large scale fuel tube manufacture. The present Mo tube production processes involve sintering or gun drilling.

The Russians latched on the the Molybdenum fuel tube idea and were already investigating practical realization of it in 2015 as indicated by the paper Molybdenum Fuel Tube
 

MOLYBDENUM FUEL TUBES:
Molybdenum has a much higher thermal conductivity than HT9. Molybdenum fuel tubes potentially allow a much higher FNR power and/or a smaller temperature drop across the fuel tube wall.
 

This web page last updated November 2, 2023.