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XYLENE POWER LTD.

FNR FUEL TUBES

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

INTRODUCTION:
This web page deals with FNR fuel tubes. The main motivation for having fuel tubes is to prevent the nuclear fuel and the fission products from mixing with the reactor primary coolant. Confinement of the fuel in fuel tubes also has the effect of confining the neutron flux to the proximity of the fuel assembly, which can protect the intermediate heat exchanger and coolant enclosure tank from neutron excitation and cumulative damage.

The 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 tube fabrication, must have a small neutron absorption cross section for fast neutrons and must have a low density BCC crystal lattice throughout its operating temperature range so as to be resistant to fast neutron induced swelling.

The fuel tube material must also be chemically compatible with the fuel elements Pu and U, the heat transfer element sodium, the coolant sodium and the element zirconium which may be used to raise the melting point of Pu-Fe eutectic or may be used to suppress corrosion in reactors that use fluoride salt fuel instead of metallic fuel.

The fuel tube material must tolerate material stress caused by contained core fuel swelling, 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 liquid sodium freezing and remelting.

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

FUEL TUBE DESCRIPTION:
Each fuel tube is 0.500 inch OD X 6.0 m long. 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.

The bottom 4.3 m of each fuel tube volume contains uranium alloy fuel rods. The top 1.6 m of each fuel tube is known as the fuel tube plenum and contains spare liquid sodium and inert gas. The fuel tubes form a sealed barrier around the fuel rods which prevents intensely radioactive fuel and fission products mixing with the primary coolant and depositing on the cooler heat exchange and enclosure surfaces.
 

FUEL TUBE MATERIAL SELECTION:
With respect to the FNR design developed on this web site natural circulation of the primary liquid sodium is used to achieve mechanical simplicity. The temperature at the bottom of the primary liquid sodium pool is about 390 degrees C and the temperature at the top of the primary liquid sodium pool is about 490 degrees C. Various parts of a fuel tube normally operate in the temperature range 390 C to 498 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 390 deg C to 460 deg C HT-9 is subject to fast neutron induced embrittlement. The fuel tubes must also have sufficient wall thickness to safely accommodate the wall stress associated with fuel bundle insertion into the FNR primary liquid sodium pool while the sodium inside the fuel tubes is initially solid.

A related major issue is minimizing the fuel tube material nickel content. 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. A further disadvantage of Ni is that on neutron activation Ni-58 forms the long lived isotope Ni-59 which is a long term nuclear waste disposal problem. Hence the fuel tube alloy should have a very low nickel fraction.

Another practical consideration in choosing fuel tube material is its weldability. Each FNR has _______ 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 embrittlement. In a practical FNR the bottom 1.8 m of fuel tube operates at about 390 deg C, the top 3.4 m of fuel tube operates at about 490 deg C and there is a middle transition region up to about 0.7 m long where the temperature transition from 390 deg C to 490 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-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 core 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 is required.

Significant problems with HT-9 are poor thermal conductivity, neutron absorption and and loss strength at high temperatures. It is necessary to find a material with a comparable neutron absorption cross section, higher thermal conductivity and higher strength at high temperatures.

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

The 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.

Molybednum 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

To further improve breeding it might be necessary to shift from Na cooling to Pb-Bi cooling. The compatibility of Mo fuel tubes with Pb-Bi coolant is presently not known to this author.
 

STANDARD FUEL TUBE DIAMETER AND WALL THICKNESS:
In order to minimize neutron absorption by fuel rod metal we will attempt to design the FNR using 0.500 inch OD fuel tube with a 0.035 inch wall thickness. Hence the resulting tube ID is:
0.500 inch - 2 (0.035 inch) = 0.430 inch

The thin wall tube allows more contained fuel and transports more heat but is less able to tolerate stress related to rapid vaporization of contained sodium. The thin wall is less tolerant of physical handling problems. However, we need to use to the thin wall tube to achieve a high average plutonium concentration and a low average fuel tube metal concentration in the reactor core zone.

If the resulting internal gas pressure is too high we may have to consider use of fuel tube with a larger wall thickness. Note that as the fuel tube wall thickness changes so also does the optimum fuel rod diameter.
 

FUEL TUBE FABRICATION:
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 a prompt neutron critical condition.

The fuel rods are fabricated with end beads that have a precise 0.425 inch OD. In a prompt neutron critical condition liquid sodium in contact with the hot end of the fuel rod stack will vaporize. The confined high pressure sodium vapor will propel the core fuel rods in the fixed fuel bundles into the fuel tube plenums causing safe temporary disassembly of the core fuel.

The temperature drop across a ~ 0.035 inch thick fuel tube wall is 8 deg C. For thicker fuel tube wall (0.049 inch or 0.065 inch) the wall temperature drop is proportionately greater.

The fuel tubes are spiral wound on the outside with 20 gauge = 0.032 inch diameter chrome steel wire which is spot welded in place and serves to maintain the minimum intertube spacing while permitting up to 10% tube material linear swelling in the core zone. The spiral turn to turn distance is about 1 foot (30 cm) to laterally stabilize the fuel tubes while minimizing the coolant flow resistance. This wire winding thickness must be sufficient to ensure sufficient liquid sodium flow to a hot spot which forms gaseous coolant bubbles (voids). If voids form the buoyancy force will be increased but the coolant mass flow will be reduced. We must check that there is no region of coolant thermal instability as the coolant flow cross section decreases or the core fuel temperature increases.

Note that the desired square fuel tube array geometry is stabilized by the shroud plates and by the 45 degree diagonal plates used to form and strengthen the fuel bundle.
 

FUEL TUBE ASSEMBLY:
The fuel tubes are 0.50 inch OD vertical steel tubes 6 m tall. Note that:
240 inches X 0.0254 m / inch = 6.096 m
Tubes are supplied 240 inches +/- 1 inch and should be cut to be exactly 6.000 m long.

At the bottom of each active fuel tube is a bottom plug. Above this plug is a fuel rod stack. The lowest 1.8 m of this stack consists of 6 X 0.30 m long X 10.00 mm diameter blanket rods initially 90% uranium and 10% zirconium. Above that is 0.7 m of core fuel consisting of 2 X 0.35 m long X 9.00 mm diameter core rods 70% uranium-20% plutonium-actinide-10% zirconium alloy. Then there is 1.8 m of stack consisting of 6 X 0.30 m long X 10.00 mm diameter blanket rods initially 90% uranium and 10% zirconium.

Above the fuel rod stack is a plenum space about 1.6 m high.
 

0.035 INCH FUEL TUBE WALL THICKNESS:
In order to minimize the amount of fuel tube metal absorbing neutrons try a fuel tube wall thickness of 0.035 inch. Then the fuel tube ID is given by:
0.500 inch - 2 (0.035 inch)
= 0.500 inch - 0.070 inch
= 0.430 inch
= 10.922 mm

The corresponding optimum core rod diameter is:
0.85 X 10.922 mm = 9.2837 mm
~ 9.28 mm
We may need to settle on a 9 mm core rod diameter and a 10 mm blanket rod diameter.

Let Pm = maximum safe internal gauge pressure in the tube. Then:
Pm (0.430 inch) dL = 10,000 psi X 2 X (0.035 inch) X dL
or
Pm = 10,000 psi (0.070 inch) / 0.430 inch
= 1627.9 psi

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

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

Thus with a 0.035 inch wall thickness the maximum plenum gas working pressure will be limited to:
1627.9 psi - 41.1 psi = 1586.8 psi
 

0.049 INCH FUEL TUBE WALL THICKNESS OPTION:
In order to increase the allowable plenum gas pressure consider a fuel tube wall thickness of 0.049 inch. Then the fuel tube ID is given by:
0.500 inch - 2 (0.049 inch)
= 0.500 inch - 0.098 inch
= 0.402 inch
= 10.21 mm
Realizing the required blanket rod diameter likely requires custom silica tube molds.

The corresponding optimum core rod diameter is:
0.85 X 10.21 mm = 8.6785 mm
~ 8.68 mm
Realizing this core rod diameter likely requires custom silica tube molds.

Let Pm = maximum safe internal gauge pressure in the tube. Then:
Pm (0.402 inch) dL = 10,000 psi X 2 X (0.049 inch) X dL
or
Pm = 10,000 psi (0.098 inch) / 0.402 inch
= 2437.8 psi

The maximum height Hb of blanket rod that one atmosphere can support 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

Thus the pressure necessary to lift the upper blanket rod stack is:
(1.8 m / 0.6446 m) X 14.7 psi = 41.1 psi

Thus with a 0.049 inch wall thickness the maximum plenum gas pressure will be limited to:
2437.8 psi - 41.1 psi = 2396.7 psi
 

0.065 INCH FUEL TUBE WALL THICKNESS OPTION:
In order to further increase the allowable plenum pressure consider a fuel tube wall thickness of 0.065 inch. Then the fuel tube ID is given by:
0.500 inch - 2 (0.065 inch)
= 0.500 inch - 0.130 inch
= 0.370 inch
= 9.398 mm
The blanket rods can be formed using standard 9 mm ID silica tubes.

The corresponding optimum core rod diameter is given by:
0.85 X 9.398 mm = 7.988 mm
~ 8.00 mm
which can be realized using standard 8 mm ID silica tube molds.

Let Pm = maximum safe internal gauge pressure in the fuel tube. Then:
Pm (0.370 inch) dL = 10,000 psi X 2 X (0.065 inch) X dL
or
Pm = 10,000 psi (0.130 inch) / 0.370 inch
= 3513.5 psi

The maximum height Hb of blanket rod that one atmosphere can support 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

Thus the presure necessary to lift the upper blanket rod stack is:
(1.8 m / 0.6446 m) X 14.7 psi = 41.1 psi

Thus with a 0.065 inch wall thickness the maximum plenum gas working pressure will be limited to:
3513.5 psi - 41.1 psi = 3472.4 psi
 

FUEL ROD BEADS:
The cool end fuel rod beads should slide inside the fuel tubes with an almost airtight fit. The nominal fuel tube ID is 0.43 inches. The fuel rod beads must be made to have an OD of about 0.42 inches. The objective is to make fuel rods behave like projectiles in a blow gun. Note that the fuel rod cool end is away from the neutron flux which minimizes the effect of fast neutron induced bead swelling.
 

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 1.6 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.
 

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.
 

FUEL TUBE END PLUGS:
At the ends of each fuel tube are a seal welded plugs. The each plug has a 2.5 cm length that snugly fits inside the fuel tube and a 2.5 cm length that projects beyond the end of the fuel tube.

The fuel tube end plugs, after being cooled with liquid nitrogen, are slid into the fuel tube. Each end plug overlaps the fuel tube by 0.025 m. As the end plugs warm up their OD makes a gas tight seal to the fuel tube ID and then are seal welded in place. The bottom plugs have a slight point taper to assist in insertion and a saw cut end cross for mating to the fuel tube support grid. The top plugs each have 4 X (1 / 16) inch high bumps at 90 degree intervals about the tube axis which assist with fuel tube spacing maintenance. During insertion of the top plug into the fuel tube its angular orienntation about the fuel tube axis must be aligned with respect to the angular orientation about the fuel tube axis of the saw cuts in the bottom plug of the same fuel tube. During fuel tube insertion into a fuel bundle the bottom plug must be in the correct angular position to mate with the fuel bundle bottom grating.

Note that the seal of the fuel tube top plug, which contains inert gas at 490 C, may be 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 1 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 1 inch ID pipe by about 10 feet. At its exact balance point it will tip inside the horizontal 1 inch ID pipe.
 

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.

Define:
Ro = fuel tube outside radius
Ri = fuel tube inside radius

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 = 0.2500 inch
Ri = 0.215 inch
Sy = 30,000 lb / inch^2

Then:
Tw = {[(Ri + Ro)^2] [Ro - Ri]} {Sy / 9}
= {[(.465 inch)^2] [0.035 inch]} {30,000 lb / 9 inch^2}
= 25.2 lb - inch

This lateral torque limit is a major constraint on 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 fuel tubes must always be supported or stabilized all along their length. This issue is particularly important for road transport. This requirement imposes size and strength requirements on the fuel bundle corner girders, shroud sheets and diagonal plates which indirectly support and stabilize the fuel tubes.

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

The fuel tubes rely on the fuel bundle shrouds, diagonal plates and corner girders to accelerate the mass of the fuel, fuel tubes and the liquid sodium contained in the fuel bundles and thus prevent excessive horizontal forces on the fuel tubes. However, this fuel tube protection requirement imposes further strength requirements on the fixed fuel bundle corner girders and their mounting sockets and on the fuel bundle shrouds and diagonal plates. 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. In operation the entire liquid sodium pool rests on a layer of ball bearings and high pressure oil to isolate if 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 5.5 m above the bottom of the liquid sodium pool.
 

ASSEMBLED FUEL TUBE MASS:
Each active fuel tube contains 2 X 0.35 m long core rods and 12 X 0.30 m blanket rods.

Mass of fuel rods per active fuel tube :
(2)(0.356390 kg / core rod) + 12 (0.37425793 kg / blanket rod)
= 0.71278 kg + 4.49109516 kg
= 5.2038 kg / fuel tube.

Fuel Tube Steel:
Mass = Pi [(0.5 inch)^2 - (0.43 inch)^2] / 4 X 6.0 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3
= 1.5584216 kg

5 CM Fuel Tube End Plugs:
Mass = 2 X Pi X (.25 inch)^2 X .05 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3
= 0.099745 kg

Sodium:
Each fuel tube contains sufficient liquid sodium to cover the core and blanket rods up to a height of 4.5 m.
 

The volume of liquid sodium initially required inside a fuel tube is:
Pi [(.43 inch / 2)^2] [0.0254 m / inch]^2 [4.3 m] - Pi[(4.50 X 10^-3 m)^2 (2)(0.35 m)] - Pi [(5.0 X 10^-3 m)^2 (12)(0.30 m)]
= Pi [1.282368 X 10^-4 m^3 - 0.14175 X 10^-4 m^3 - 0.90000 X 10^-4 m^3]
= 0.240618 X 10^-4 m^3

The mass of this sodium is:
0.240618 X 10^-4 m^3 X 927 kg / m^3 = 0.022305 kg
 

TOTAL ACTIVE FUEL TUBE MASS:
For each fuel tube:
Fuel Rods + tube steel + end plug steel + sodium
5.2038 kg + 1.5584216 kg + 0.099745 kg + 0.022305 kg = 6.88427 kg
 

FUEL DETAIL:
In each fuel tube the FNR top and bottom blanket fuel rod stacks are each:
2(.29 m) + 2(.30 m) + 2(.31 m) = 1.8 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 allow easy fuel rod mechanical sorting and to prevent accidents resulting from fuel rod type mix ups.

The FNR core fuel rods are initially 2 X 0.35 m long but over time may swell to average lengths of 2 X 0.4117 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 0.3 m long X 10.00 mm diameter beaded blanket rods initially consisting of 90% uranium and 10% zirconium and 2 X 0.35 m long X 9.00 mm diameter beaded core rods initially consisting of 70% uranium-20% plutonium-actinide-10% zirconium alloy.

Passive fuel tubes contain 14 X 0.3 m long X 10.00 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
= [(0.035 inch) / (0.215 inch)] 68.7 MPa
= 11.184 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.
 

POTENTIAL 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. A potential solution to this brittleness issue is to periodically run the reactor at no load to heat the entire liquid sodium pool up to 545 degrees C to anneal the fuel tubes.
 

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:
PROPERTY316LHT-9FeCr
Rho7966 kg / m^3 7.874 kg / m^3
TC @ 25 C15 W / m-K26.2 W / m-K80.4 W / m-K93.9 W / m-K
TC @ 500 C15 W / m-K26.2 W / m-K
TCE @ 25 C18 X 10^-6 / K15 X 10^-6 / K11.8 X 10^-6 / K4.9 X 10^-6 / K
TCE @ 500 C18 X 10^-6 / K15 X 10^-6 / K4.9 X 10^-6 / K
Y @ 25 C, no rad.-2000 GPa?211 GPa279 GPa
Y @ 250 C, no rad.-2000 GPa?
Y @ 250 C, with rad.2000 GPa?
Bulk Y @ 500 C120 GPa
Sy @ 25 C, no rad.291.3 MPa-400 MPa
Sy @ 250 C, no rad.600 MPa200 MPa
Sy @ 250 C, rad900 MPa
Sy @ 400 C, rad600 MPa to 900 MPa
Sy @ 500 C, no rad167 MPa400 MPa to 550 MPa
Sy @ 500 C, with rad450 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 NumberSymbolMASS % of fission productsMPBPGAS at 500 C?
31Ga0.03829.78 C2403 CN
32Ge0.328937.4 C2830 CN
33As0.526__613 C?
34Se2.002217 C685 C?
35Br2.092- 7.2 C58.78 CY
36Kr5.746- 156.6 C- 152.3 CY
37Rb4.42838.89 C686 C?
38Sr9.307769 C1384 CN
39Y 4.587819 C1194 CN
40Zr10.9461852 C4377 CN
41Nb3.8621024 C3027 CN
42Mo3.7852610 C5560 CN
43Tc0.4942157 C4265 CN
44Ru0.24638.89686?
45Rh0.0481966 C3727 CN
46Pd0.0771554 C2970 CN
47Ag0.042962 C2212 CN
48Cd0.208320.9 C765 CN
49In0.381156.6 C2080 CN
50Sn4.191231.88 C2260 CN
51Sb3.848630.74 C1750 CN
52Te7.667452 C1390 CN
53I 4.657113.5 C184.35 CY
54Xe8.799- 111.9 C- 107.1 CY
55Cs4.29428.40 C669.3 C?
56Ba6.409725 C1640 CN
57La1.886921 C3457 CN
58Ce2.195799 C3426 CN
59Pr0.431931 C3512 CN
60Nd0.4381024 C3027 CN
61Pm0.041
62Sm0.0111077 C1791 CN
63Eu0.001822 C1597 CN
64Gd0.0001313 C3266 CN
65Tb0.0001360 C3123 CN
66Dy0.0001412 C2562 CN

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 = 2 (0.356390 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 2 (0.356390 kg)
 

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 2 (0.356390 kg) X 5.746 X 10^-2

The atomic weight of krypton is: 83.798

The number of moles of krypton produced is:
[ Fb 2 (0.356390 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 2 (0.356390 kg) (8.799 X 10^-2)

The atomic weight of xenon is: 131.293

The number of moles of xenon produced is:
[Fb 2 (0.356390 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 2 (0.356390 kg) (5.746 X 10^-2) X 1000g / kg] / [83.798 g / mole]
+ [Fb 2 (0.356390 kg) (8.799 X 10^-2) X 1000 g / kg] / [131.293 g / mole]
= [Fb 2 (0.356390) [(57.46 / 83.798) + (87.99 / 131.293)] moles
= [Fb 2 (0.356390) [(0.6857) + (0.6702)] moles
= 0.96646 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 10.016 MPa occupies a volume of:
(22.4 X 10^-3 m^3 / mole) X (784 K / 273 K) X (0.101 MPa / 10.016 MPa)
= 0.648677 X 10^-3 m^3 / mole

Hence the plenum volume required for storage of inert gas fission products at 511 C and 10.01 MPa is:
(0.648667 X 10^-3 m^3 / mole) X (0.96646 Fb) moles inert gas)
= (0.62690 Fb) X 10^-3 m^3

The inside cross sectional area of the fuel tube is given by:
Pi (0.43 inch / 2)^2 X (.0254 m / inch)^2
= 0.9369 X 10^-4 m^2

Hence the minimum dedicated plenum length required for inert gas storage is:
[(0.62690 Fb) X 10^-3 m^3] / 0.9369 X 10^-4 m^2]
= 6.6913 Fb m

For Fb = 0.15 the dedicated plenum length required for inert gas storage is:
6.691 Fb m = 1.003 m
which is consistent with the 1.6 m of available plenum height in the fuel tubes.

The dedicated gas portion of the plenum limits 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 .43 inch) / 2)^2 - [(.43 inch)/ 2]^2} X 0.7 m X (.0254 m / inch)^2
= Pi{ [.0611325625 - .046225] inch^2} X 0.7 m X (.0254 m / inch)^2
= 2.115 X 10^-5 m^3

The length of plenum required for this extra liquid sodium is:
2.115 X 10^-5 m^3 / 0.9369 X 10^-4 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)
= 1.003 m + 0.2257 m
= 1.229 m

However, the available plenum height is 1.6 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 primary liquid sodium.
 

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 CNa VAPOR PRESSURE IN ATMOSPHERES
10473.78
11758.34
123211.20
139925.50
146833.30
152241.27

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 8 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:
8.0 deg C X 26.2 W / m-deg C / (.035 inch X .0254 m / inch) = 235,770 W / m^2

The minimum core zone fuel tube external surface area for a reactor is about :
Pi X (.500 inch) X (.0254 m / inch) X 0.35 m / tube X 330,016 active fuel tubes
= 4608.47 m^2

Hence the corresponding maximum allowable reactor thermal power set by thermal conduction through fuel tube walls with 0.35 m of core fuel rods in the core region and a 8 deg C fuel tube wall temperature drop is:
235,770 W / m^2 X 4608.47 m^2
= 1,086,538,644 Wt
= 1,086.5 MWt

Note that this thermal power limit is dependent on the thickness of the middle core region. At relatively low Pu concentrations this region may be as thick as 0.70 m whereas at higher Pu concentrations this region might be thinner than 0.35 m. The actual region 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 is limited by the liquid sodium chimney effect.
 

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. Assume a 2 deg C temperature drop across the fuel tube wall. Thus the maximum safe continuous operating heat flux through the Mo fuel tubes of the reactor core is:
2.0 deg C X 138 W / m-deg C / (.035 inch X .0254 m / inch) = 310,461 W / m^2

The minimum core zone fuel tube external surface area for a reactor is about :
Pi X (.500 inch) X (.0254 m / inch) X 0.35 m / tube X 330,016 active fuel tubes
= 4608.47 m^2

Hence the corresponding maximum allowable reactor thermal power set by thermal conduction through fuel tube walls with 0.35 m of core fuel rods in the core region and a 2 deg C fuel tube wall temperature drop is:
310,461 W / m^2 X 4608.47 m^2
= 1,430,751,091 Wt
= 1,431 MWt

Note that this thermal power limit is dependent on the thickness of the middle core region. At relatively low Pu concentrations this region may be as thick as 0.70 m whereas at higher Pu concentrations this region might be thinner than 0.35 m. The actual region 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 is limited by the liquid sodium chimney effect. Thus the reactor power benefits of Mo fuel tubes are significant.
 

This web page last updated March 22, 2021.

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