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

This web page deals with metallic FNR fuel rods. Important issues with these fuel rods are that:
a) As shown at FNR Fuel Tube Wear use of metallic fuel rods prevents long term internal corrosion of FNR Fuel Tubes;
b) The required Pu concentration in core fuel rods is readily achieved via electrolytic fuel reprocessing;
c) The fuel rods are compatible with sodium bonding;
d) The fuel rod lengths are compatible with vacuum casting;
e) The fuel rods can be cast using silica tube forms;
f) The fuel rod diameter must be sufficient as compared to surrounding sodium and steel to ensure a negative reactivity temperature coefficient;
g) The melting point of the core fuel rod external surface must be above the melting point of the sodium inside the fuel tube. This may be a challenge when the plenum pressue is high.

The FNR core fuel rods are initially nominally an alloy consisting of 70% metallic U-238, 20% Pu-239 and 10% zirconium by weight. The purpose of the Pu-239 is to fuel the nuclear reaction. The purposes of the U-238 are to absorb surplus neutrons to breed more Pu-239 and to dilute the Pu-239. The purpose of the 10% zirconium is to prevent formation of a low melting point eutectic (410 deg C at an iron atom fraction of 0.1) between plutonium and iron. (Til & Yoon P.105 - 106) and Hofman et al 1996. The fraction of Zr cannot be further increased due to an upper limit on the fuel rod material melting point imposed by use of silica tubing molds for casting the fuel rods. However, it might be necessary to raise this melting point by use of a different mold material.

Note that when a fissile fuel rod is cast the outer surface cools before the inside. Then when the FNR is operated center line melting occurs. The U component tends to concentrate around the outer perimeter of the fuel rod and Pu-Zr tends to concentrate in the middle of the fuel rod.

During fission heat is emitted mainly by the Pu so the core fuel rod center line temperature is hotter than would be the case if the Pu was uniformly distributed through the fuel rod. This situation can be modelled by a Pu-Zr core and a U surround. The melting point of the U surround is 1134 degrees C. When there is a pressure of more than 6 bar in the fuel tube plenum the U surround will melt before the sodium internal to the fuel tube boils. However, we must take into account thermal expansion of the sodium internal to the fuel tube in the temperature range 500 C to 1134 C.


At 15% fuel burnup:
20%(initial average Pu fraction) - 15%(burnup) + 7.7% (U-238 to Pu-239 conversion) = 12.7%

Note that a key reactor design requirement is that when the movable fuel bundles are fully inserted the core zone achieves criticality with an average Pu-239 fraction in the core fuel of 12.7%. This core zone criticality requirement is checked on the web page titled: FNR CRITICALITY

The melting points of the fuel rod elemental components are:
Pu = 639.4 deg C
U = 1134 deg C
Zr = 1855 deg C.

The fuel rod casting process involves relatively rapid cooling of the entire fuel rod, so that during the casting process the U, Pu and Zr remain uniformly distributed.

Hoffman ________has shown that during fuel rod use in a FNR the Zr in the central portion of the fuel rod moved radially toward the fuel rod center displacing U and leaving a Zr depleted U enriched region in a ring around the fuel rod center. This behavior is likely a result of melting of the central portion of the fuel rod. When the melt cooled, which due to the large thermal mass of the surrounding liquid sodium coolant likely occured over a long period of time, the outer part of the melt was cooler than the center and the fusing U-Pu alloy excluded Zr, which caused Zr to concentrate along the fuel rod center line. This action raised the melting point on the fuel rod center line but lowered the melting point in the Zr depleted ring. The subsequent fuel rod thermal expansion was then dominated by the character of the ring around the fuel rod center which contains no Zr and contains U-Pu enriched in U.

However, we cannot operate the fuel close to the melting point of this ring due to the large thermal coefficient of expansion due to Pu phase changes below its melting point. The resulting tensile hoop stress on the outer portion of the fuel rod will likely crack the fuel rod material and might cause the fuel rod diameter to expand so much that the fuel rod can no longer slide inside the fuel tube.

The aformentioned rapid expansion of the U-Pu alloy will commence at the temperature at which the alloy becomes phase unstable. This phase transition point is 560 degrees C.

In summary, when fuel rod center line melting occurs the fuel forms a ring around its center line that is depleted in Zr. From that time forward the radial thermal expansion of the fuel rod is dominated by the thermal expansion of that ring when its temperature exceeds 560 degrees C. We do not know the radius of the Zr depleted ring, so for certainty in FNR design we need to assume that its radius is small. Hence we need to design the FNR to have a maximum fuel center line temperature of 560 degrees C.

The stable U-Pu phase of interest is below 560 degrees C for uranium atom fractions in the range 0.74 to 0.85.

The importance of phase stability is that when the phase changes the alloy becomes less dense. A decrease in fuel rod density near its center leads to large tensile hoop stress near the rod outer surface. We do not want the fuel rod to crack in a manner that jams it in the fuel tube. Hence 560 degrees C is the maximum allowable temperature along the fuel rod center line.

The issue of a potential interaction between the plutonium and the iron in the fuel tube is mitigated by:
a) Keeping the U-Pu fuel in a stable phase at all times;
b) Ensuring that the steel fuel tube wall is sufficiently thick to safely accommodate any low temperature Pu-Fe eutectic that does form;
c) By adding up to 10% Zr to raise the U-Pu-Zr eutectic melting point as high as the silica fuel rod casting forms will permit.

A problem with Zr addition is that it likely will not be uniformly incorporated into the fuel crystal structure. However, uranium-zirconium alloys are phase stable below 607 degrees C.

The melting point of binary couple Pu-Zr increases with increasing Zr fraction. The lowest melting point of this couple is 639.4 degrees C.

Of all the aforementioned temperature constraints the dominant one is the 560 degree C constriant for a phase stable U-Pu alloy. Hence for core fuel stability we need to keep the temperature on the fuel center line less than 560 degrees C.

An important issue in FNR design is the full load temperature difference between the fuel rod center line and the adjacent cooling sodium. A FNR with fuel rods on a square grid has four sodium filled cooling channels associated with each fuel tube. In order to make the FNR durable it must be able to safely function with two of these cooling channels blocked. Under that circumstance the temperature difference between the fuel rod center line and the sodium will be twice its normal value. To prevent fuel damage the maximum allowable fuel center line temperature is 560 degrees C. Hence in order to realize a primary sodium discharge temperature of 460 degrees C at full load the normal temperature difference between the fuel rod center line and the sodium is limited to 50 degrees C. That temperature difference in combination with the fuel dimensions results in a power per unit fuel rod length. From that power we can calculate the required core zone thickness. From that thickness we can calculate the minimum required Pu-239 concentration in the fuel rods.

R = radius from fuel rod center line;
Ro = core fuel rod radius = 3.27 mm;
Rt = average tube radius = (.1875 + .1515) / 2 = 0.1695 inch = 4.30 mm
Tf = fuel rod temperature at radius R from its center line;
Tfc = temperature on the center line of the core fuel rod;
Tfs = temperature on the surface of the core fuel rod;
Kc = thermal conductivity of the core fuel rod material with bubbles;
L = length of core fuel rod;
H = thermal power per unit volume generated within the fuel rod;
P = total thermal power generated in the core fuel rod;

P = Pi Ro^2 L H
H = P / (Pi Ro^2 L)

Thermal balance at radius R gives:
Pi R^2 L H = 2 Pi R L (- dTf / dR) Kc
R H = 2 (- dTf / dR) Kc
R dR = 2 (-dTf) Kc / H or
Ro^2 / 2 = 2 (Tfc - Tfs) Kc / H

Substituting for H gives:
Ro^2 / 2 = 2 (Tfc - Tfs) Kc (Pi Ro^2 L)/ P
1 / 2 = 2 (Tfc - Tfs) Kc (Pi L) / P

Rearranging this equation gives:
(Tfc - Tfs) = (P / L)[1 / 4 Kc Pi)]
which is the temperature difference between the fuel rod center line and the outside surface of the core fuel rod. Note that this result is independent of the fuel rod rdius.

Due to formation of fission product gas bubbles in the core fuel ASSUME:
Kc ~ (Kcb / 2)
where Kcb is the thermal conductivity of core fuel material not containing fission product gas bubbles.

For uranium:
Kcb = 27.5 W / m deg C

Kc = Kcb / 2
= (27.5 W / m deg C) / 2
= 13.75 W / m deg C

(Tfc - Tfs) = (P / L)[1 / (4 Kc Pi)]
= (P / L)[1 / (2 Kcb Pi)]
= [3336 W / .389 m][1 / (2 X 27.5 W / m deg C X 3.14159)]
= 49.63 degrees C
~ 50 degrees C

As shown on the web page titled FNR Geometry the total number of active fuel tubes is 299,776.

Hence to achieve 1000 X 10^6 Wt each active fuel tube must output:
P = 1000 X 10^6 W / 299,776 active fuel tubes = 3335.8 W / active fuel tube.

L = minimum fuel rod overlap that comes from holding the maximumtemperature drop across the fuel tube wall at 10 degrees C.

Thus the maximum temperature drop from the fuel rod center line to the adjacent sodium is 60 degrees C

In order to have a range of adjustment the core fuel rods must be 0.6 m long.

If there is a beyond specification high temperature transient there will be fuel center line phase change but the fuel center line temperature must increase by a further
605 C - 560 C = 45 degrees C
to enable plutonium phase change anywhere in the uranium and by
607 C - 560 C = 47 C
to enable zirconium mobility anywhere in the uranium.

Assume 20% Pu, 70% U:
Fp = weight fraction of Pu-239 in fuel
Fu = weight fraction of U-238 in fuel
Then initially:
Fu / Fp = 7 / 2
= 3.5
Fu + Fp = 0.90

Assume that during the fuel cycle there is 15% core rod burnup. Then due to Pu-239 fissioning the core rod Pu-239 initial fraction drops from 20% to 5% but due to new Pu-239 formation the core rod Pu-239 concentration increases by:
[(number of Pu-239 atoms formed) / (number of Pu-239 atoms fissioned)] X 15%
= [(number of U-238 atoms)(U-238 fast neutron capture cross section) / (no. of Pu-239 atoms)(Pu-239 fast neutron fission cross section)] X 15%
= [(70)(0.25 b) / (20)(1.7 b)] X 15%
= 7.72%

Hence the final Pu-239 concentration is about:
(5% + 7.72%) = 12.72%

We must check that the reactor core can remain critical at this Pu-239 fraction. There will be some neutron absorption by fission products, fuel bundle steel, liquid sodium and blanket U-238.

The nominal fuel tube ID is:
0.303 inches
= 7.696 mm.
Note that this is a standard steel tube ID. The reactor core fuel rods are:
0.85 X 7.696 mm = 6.542 mm
nominal diameter that loosely slide into the steel fuel tubes. Note that the core rods are thinner than the blanket rods which permits a longer core rod than a blanket rod. For a core rod to slide into the fuel tube the maximum deviation of a fuel tube from being dead straight is:
7.696 mm - 6.542 mm = 1.154 mm over a length of 600 mm.

The core rods need to have an integral bead at the cool end of the fuel rod. The function of this bead is to provide a nearly gas tight sliding fit with the inside diameter of the fuel tube. To enhance this gas seal steel ball bearings sized to match the fuel tube ID are used to separate the blanket rods. Hence when high pressure sodium and cesium vapor are produced during a prompt critical instant they are confined rather than leaking out via the gap between the blanket rod OD and the fuel tube ID.

The blanket fuel rods are nominally 7.0 mm in diameter. For a blanket rod to slide into a fuel tube the maximum deviation of a fuel tube from being dead straight is:
7.696 mm - 7.0 mm = 0.7 mm over a blanket fuel rod length of 0.36 m

The nominal core fuel relative smear density is:
[0.85]^2 = 0.6792

This smear density allows for experimentally observed fuel swelling. Inside the steel fuel tubes, along with the fuel rods is liquid sodium, which provides a good thermal contact between the fuel rods and the steel fuel tubes independent of the core fuel rod diameter and which chemically absorbs the otherwise gaseous and corrosive fission products iodine and bromine.

There is another issue which is essential for FNR safety approval. If a FNR goes prompt critical within about 10^-4 seconds sodium and cesium, which are in direct contact with the fissile fuel inside the fuel tube, vaporize. This vapor pressure acts like the propellant in a gun and drives part of the fissile fuel and blanket fuel toward the fuel tube plenum.

The resulting change in fissile fuel geometry is sufficient to suppress a minor unplanned temporary injection of positive reactivity. This effect is mentioned in Hofman et al 1996. For safety certainty the reactor should have instrumentation that detects the gamma pulse associated with the prompt critcality and immediately activates a mechanical system that injects a large amount of negative reactivity. The issue is thatā¬ as the sodium and cesium vapor leak past the top of the fissile fuel and condense gravity may cause the movable fissile fuel to fall back toward the prompt critical state. To avoid another prompt critical pulse it is necessary to immediately mechanically change the fuel geometry to reduce the reactivity of the relevant fuel bundles.

Due to more fuel rods in fixed bundles than in movable bundles the reactivity in the space immediately above the core zone is higher than the reactivity in the space immediately below the core zone. Hence the change in core zone reactivity related to driving fuel into the plenum of fixed fuel bundles is relatively large. this effect is favorable in terms of triggering a prompt critical shutdown.

The core fuel rods are fabricated with a bead at the cool end. In a prompt neutron critical condition the core zone fuel becomes very hot causing rapid vaporization of the adjacent and embedded liquid sodium and cesium. There are ball bearings in the blanket rod stack on either side of the core zone fuel. The resulting sodium and cesium vapor pressure tends to disassemble the core fuel. The ball bearings are snug to the fuel tube ID and improve the fuel disassembly characteristics. A prompt neutron critical condition will cause a sudden heat pulse that will vaporize the Na and any Cs in contact with the fuel. The ball bearing OD must closely match the fuel tube ID. The vapor pressure will tend to propel fixed fuel bundle blanket rods above the core zone upward toward the fuel tube plenum.

The net effect of this sodium and cesium vaporization is to cause axial fuel disassembly which will reduce the fissile fuel concentration in the core zone.

The blanket fuel rods are initially 90% uranium plus 10% zirconium. Zirconium is used to prevent formation of a Pu-Fe eutectic. Since fissioning in the blanket rods is minimal their nominal initial outside diameter is 7.0 mm, which is about 91% of the initial fuel tube ID. There must be sufficient clearance between the blanket fuel rod OD and the fuel tube ID to allow for fabrication tolerances and for a loose sliding fit. The objective is to make the blanket fuel rods located above the ball bearings move toward the plenum like blowgun projectiles. Projectile braking is achieved by compression of the gas trapped in the fuel tube plenum. Note that this process is performance limited by the fuel tube hoop stress rating.

In order for the sodium vapor to lift the weight of the stack of fuel rods above it the vapor pressure must reach a minimum of about:
(1.8 m + 0.6 m) / (0.646 m Atmosphere) = 4 atmospheres.
The internal sodium temperature in contact with the core fuel must reach about 1000 degrees C.

This pressure and temperature increase with time as inert gas pressure accumulates in the fuel tube plenum.

Thus the practical effect of the sodium vapor expansion due to prompt neutron criticality is to blow the blanket rods in the fixed fuel bundles toward the plenum spaces, thus allowing core fuel rapid axial expansion. Note that for this mechanism to work reliably the core rod should be a single piece with an end bead. Ideally the core fuel rod should be able to slide within the fuel tube.

On average the core fuel rods are initially by weight 10% zirconium, 20% plutonium and 70% uranium by weight. The density of zirconium is:
6.52 gm / cm^3
The density of plutonium is about:
19.8 gm / cm^3
The density of uranium is about 18.9 gm / cm^3

Vz = volume of zirconium in a core rod
Vp = volume of plutonium in a core rod
Vu = volume of uranium in a core rod.
Mz = mass of zirconium in a core rod
Mp = mass of plutonium in a core rod
Mu = mass of uranium in a core rod

Total volume V is given by:
V = Vz + Vp + Vu

Core fuel rod mass M is given by:
M = Mz + Mp + Mu

Mz = 0.1 M
Mp = 0.2 M
Mu = 0.7 M

Mz / Vz = 6.52 gm / cm^3
Mp / Vp = 19.8 gm / cm^3
Mu / Vu = 18.9 gm / cm^3

The average initial core rod density is:
M / V = (Mz + Mp + Mu) / (Vz + Vp + Vu)
= (Mz + Mp + Mu) / ((Mz / 6.52) + (Mp / 19.8) + (Mu / 18.9))
= M / [(0.1 M / 6.52) + (0.2 M / 19.8) + (0.7 M / 18.9)]
= 1 / ((0.1 / 6.52) + (0.2 / 19.8) + (0.7 / 18.9))
= 1 / (.015337 + .010101 + .037037)
= 1 / .062475
= 16.006 gm / cm^3

The density of mercury at room temperature is:
13.6 gm / cm^3

Hence the maximum length of a core rod made by vacuum casting is:
(13.6 / 16.006) X 760 mm = 646 mm
= 0.646 m

Thus it is practical to design a FNR with core rods up to about 0.60 m long.

The preferred method of fuel rod fabrication is vacuum casting from a liquid alloy melt. A silica tube is used as the mold. The lower end of the tube is dipped in the liquid alloy and a vacuum is applied to the upper end of the tube. If the furnace pressure is one atmosphere the alloy will rise in the tube. The maximum height of that rise is:
76 cm X (density of mercury) / (density of alloy)
= 76 cm X (13.6 g / cm^3) / (16.006 gm / cm^3) = 64.57 cm

This fuel rod fabrication method limits the maximum posssible length of each fuel rod.

However, this length is further reduced by the vapor pressure at the alloy melt temperature of impurities in the alloy melt. There is a further issue that it is desirable to be able to easly sort used fuel rods based on their length. The blanket rods are much shorter than the core fuel rods. For economy in blanket rod formation try to get two blanket rods out of each cast. Hence the blanket rods should each be made 30 cm long. The core rods can each be initially 60 cm long.

The core fuel rod height must be enough that the reactor can go critical when the Pu weight fraction in the fuel is as low as 12.7%. The core fuel rods must provide for sufficient heat transfer to the liquid sodium at partial fuel bundle overlap when the average Pu weight fraction in the fuel is as high as 20%. The maximum amount of heat that can be removed from the fuel rod stack is limited by the chimney effect operating through the differential temperature of:
(460 C - 400 C) = 60 C
over a chimney height of 3.8 m.

Note that if the natural circulation is sufficient the sodium flow through the fuel will exceed the required minimum flow, causing the temperature drop across the fuel stack at a particular reactor power to decrease. It is important to limit the reactor power by limiting the maximum nitrate salt flow rate.


The core rods should not be too long to avoid tying up the available inventory of fissile material.

Each fuel tube contains sufficient liquid sodium to cover the core and blanket rods up to at least a height of 4.3 m to ensure good thermal contact between the fuel rods and the enclosing fuel tube.

The steel fuel tube initial ID is 0.303 inches. The initial core fuel rod diameter is 6.54 mm. Hence the smear density (Till & Yang P. 123) is:
[0.85]^2 X 16.006 g / cm^3 = 11.564 g / cm^2

In terms of allowance for linear core fuel rod swelling:
[1 / 0.85] = 1.1764
17.64% linear core rod swelling before the core fuel causes significant hoop stress on fuel tube walls.

The mass of each core fuel rod is given by:
Pi X (6.54 X 10^-3 m / 2)^2 X 0.60 m / rod X 16.006 g / cm^3 X 10^6 cm^3 / m^3 X 1 kg / 10^3 g
= 0.3226 kg / core rod

Core rod mass = 299,716 active fuel tubes X 0.3226 kg / core rod
= 96,691 kg
= 96.7 tonnes

With an additional 20% for the cooling section allowance results in:
1.2 X 95.625 = 114.75 tonnes of FNR core fuel.

Assume that over the core rod working life 15% of its contained Pu and U atoms fission. The mass of these fissioning atoms is:
0.9 X 0.15 X 0.3226 kg = 43.55 g

The number of fissioning atoms is:
43.55 g X 6.023 X 10 23 atoms / 239 g = 1.0975 X 10^23 atoms.

The fission energy yielded is about:
1.0975 X 10^23 fissions X 200 MeV per fission X 1.602 X 10^-19 J / eV X 10^6 eV / MeV
= 351.64 X 10^10 J
= 351.64 X 10^10 Wt - s
= 351.64 X 10^7 kWt - s
= 351.64 X 10^7 kWt -s X (1 h / 3600 s) x (1 yr / 8766 h)
= 111.42 kWt-yr

Thus if each core fuel rod has a 3.3 kWt thermal load the time between required successive core fuel rod changes is:
111.42 kWt - year / 3.3 kWt = 33.76 years

In order to allow for practical fuel bundle cooling and reprocessing we can divide a 30 year core fuel life into 5 X 6 year periods.

with (3 / 8) inch OD fuel tubes:
Average mass Mu of U-238 in each core fuel rod is:
Mu = .7 (0.3226 kg)
= .22582 kg

Average mass of Pu in each core fuel rod is:
Mp = 0.2 (0.3226 kg)
= 0.06452 kg

Mass Mz of Zr in each core fuel rod is:
Mz = 0.1 (0.3226 kg)
= 0.03226 kg

This plutonium can be obtained by reprocessing of spent CANDU fuel.

The Pu or TRU requirement per FNR is:
1.2 X 299,716 core rods X 0.3226 kg / core rod X 0.2 kg Pu / kg core rod
= 23,205 kg
= 23.2 tonnes

In 2024 the amount of TRU readily available from spent CANDU fuel is about:
0.004 X 60,000 tonnes = 240 tonnes. Hence there is presently enough plutonium available to start about:
240 tonnes / (23.2 tonnes / reactor) ~ 10 FNRs.
It is clear that in FNR planning a very important objective is breeding additional TRU for starting future FNRs.

The blanket rods must slide easily into the fuel tubes but are subject to much less swelling because their only fissionable content comes from breeding. Hence the initial blanket rod diameter is:
10.000 mm

The blanket rods rely on:
0.300 inch OD = 7.62 mm OD
cool end beads for high pressure sodium vapor to propel the fixed fuel bundle blanket rods into the fuel tube plenums on the occurance of prompt neutron criticality.

The blanket fuel rods are nominally 10% zirconium, 90% uranium by weight.
The density of zirconium is:
6.52 gm / cm^3
The density of uranium is about 18.9 gm / cm^3

Vzb = volume of zirconium in a blanket rod
Vub = volume of uranium in a blanket rod.
Mzb = mass of zirconium in a blanket rod
Mub = mass of uranium in a core rod

Total volume V is given by:
Vb = Vzb + Vub

Blanket fuel rod mass Mb is given by:
Mb = Mzb + Mub

Mzb = 0.1 Mb
Mu = 0.9 Mb

Mzb / Vzb = 6.52 gm / cm^3
Mub / Vub = 18.9 gm / cm^3

The average blanket rod density is:
Mb / Vb = (Mzb + Mub) / (Vzb + Vub)
= (Mzb + Mub) / ((Mzb / 6.52) + (Mu / 18.9))
= Mb / ((0.1 Mb / 6.52) + (0.9 Mb / 18.9))
= 1 / ((0.1 / 6.52) + (0.9 / 18.9))
= 1 / (.015337 + .047619)
= 1 /.062956
= 15.884 gm / cm^3

The mass of an average blanket fuel rod is given by:
Pi X (7.00 X 10^-3 m / 2)^2 X 0.30 m / rod X 15.884 g / cm^3 X 10^6 cm^3 / m^3 X 1 kg / 10^3 g
= 0.18292 kg / blanket rod

Mass Mub of U-238 in each average blanket fuel rod is:
Mub = .9 (0.18292)
= .1646 kg

Mass of Zr in each average blanket fuel rod is:
Mzb = 0.1 (0.18292 kg)
= 0.018292 kg

This web page last updated November 1, 2023

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