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**INTRODUCTION:**

This web page deals with FNR fuel rods.

**FUEL ROD ALLOYS:**

The FNR core rods are initially by weight 70% metalic U-238 with 20% Pu-239 and 10% zirconium alloyed with it. The purpose of the 10% zirconium is to prevent formation of a low melting point eutectic between plutonium and iron. (Til & Yoon P.105 - 106). The purpose of the Pu-239 is to fuel the nuclear reaction. The purpose of the U-238 is to absorb surplus neutrons to breed more Pu-239.

Idealy the ratio of U-238 to Pu-239 should be chosen so that this ratio stays approximately constant over the workiing life of a core fuel rod. For every Pu-239 atom fissioned a new Pu-239 atom should be formed via neutron capture by U-238. Hence ideally the rate of of a fast neutron capture by U-238 in the reactor core should equal the rate of Pu-239 fission in the reactor core. Hence ideally:

(no. of U-238 atoms)(U-238 fast neutron capture cross section) = (no. of Pu-239 atoms)(Pu-239 fast neutron fission cross section)

or

(no. of U-238 atoms) / (no. of Pu-239 atoms)

= (Pu-239 fast neutron fission cross section) / (U-238 fast neutron capture cross section)

= 1.7 b / 0.25 b
= 6.8

Let:

Fp = fraction of Pu-239

Fu = fraction of U-238

Then:

Fu / Fp = 6.8

Fu + Fp = 0.90

giving:

7.8 Fp = 0.9

or

Fp = 0.115, Fu = .785

The problem with this result is that it indicates a final Pu-239 concentration in the reactor core that is likely barely sufficient to maintain a chain reaction. To solve this problem the initial Pu-239 fraction is initially set at 20% and the initial U-238 fraction is initially set at 70%. Hence initially:

(no. of U-238 atoms) / (no. of Pu-239 atoms) = 70 / 20 = 3.5

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:

[(rate of Pu-239 formation) / (rate of Pu-239 fission)] X 15%

= [(no. 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 remains critical at this Pu-239 fraction. There will be some neutron absorption by fission products.

**FUEL ROD GEOMETRY:**

The reactor core fuel rods are 8.08 mm diameter metallic rods that loosely slide into the steel fuel tubes. The core rod diameter is intentionally only about 86% of the steel fuel tube initial ID. 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 and which chemically absorbs the otherwise gaseous reaction products iodine and bromine.

The blanket rods are initially 90% uranium plus 10% zirconium. Since fissioning in the blanket rods is minimal their initial outside diameter is 9.0 mm, which is about 4.2% less than the initial fuel tube ID.

**FUEL ROD DISTRIBUTION:**

At the bottom of each active fuel tube is a bottom plug. Above this plug are **4 X 0.600 m long X 8.93 mm diameter blanket rods** initially consisting of 90% uranium and 10% zirconium, **1 X 0.35 m long X 8.08 mm diameter core rod** initially consisting of 70% uranium-20% plutonium-actinide-10% zirconium alloy.

Each fuel tube contains sufficient liquid sodium to cover the core and blanket rods up to a height of 2.8 m to ensure good thermal contact between the fuel rods and the enclosing steel tube.

**CORE FUEL RODS:**

The steel fuel tube initial ID is 0.37 inches. Hence allowing for 74% smear density (Till & Yang P. 123) the initial core fuel rod diameter is:

[(.74)^0.5] (0.37 inch) X 25.4 mm / inch = 8.08 mm

In terms of allowance for core fuel rod swelling:

1 / [(0.74)^0.5] = 1.162

or

** 16.2% linear core rod swelling before there is significant stress on fuel tubes.**

The core fuel rods are initially 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 mass of each core fuel rod is given by:

Pi X (8.08 X 10^-3 m / 2)^2 X 0.35 m / rod X 16.006 g / cm^3 X 10^6 cm^3 / m^3 X 1 kg / 10^3 g

= **0.28725 kg / core rod**

Hence:

Mass Mu of U-238 in each core fuel rod is:

**Mu** = .7 (0.287252 kg)

= **.20107 kg**

Mass of Pu in each core fuel rod is:

**Mp** = 0.2 (0.287252 kg)

= **0.05745 kg**

Mass of Zr in each core fuel rod is:

**Wz** = 0.1 (0.287252 kg)

= **0.0287252 kg**

The total mass of Pu in the reactor is:

(0.05745 kg / core rod) X (556 core rods / active fuel bundle) X (532 active bundles / reactor) = 16,993 kg

= **16.993 tonnes**

**BLANKET FUEL RODS:**

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:

(0.37 inch X 0.95) X 25.4 mm / inch = 8.93 mm

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 each blanket fuel rod is given by:

Pi X (8.93 X 10^-3 m / 2)^2 X 0.600 m / rod X 15.884 g / cm^3 X 10^6 cm^3 / m^3 X 1 kg / 10^3 g

= **0.59690 kg / blanket rod**

Hence:

Mass Mub of U-238 in each blanket fuel rod is:

**Mub** = .9 (0.397935 kg)

= **.53721 kg**

Mass of Zr in each blanket fuel rod is:

**Mzb** = 0.1 (0.53721 kg)

= **0.053721 kg**

**CORE AND BLANKET FUEL RODS:**

The total number of core fuel rods is:

532 active bundles / reactor X 476 active fuel tubes / active bundle X 1 core rod / active fuel tube = **253,232 core fuel rods**

The number of 0.6 m long blanket rods contained in active bundles is:

532 active bundles X 476 active tubes / active bundle X 4 blanket rods / active tube = 1,012,928 blanket rods

The number of blanket rods contained in the passive blanket bundles is:

272 passive bundles X 556 fuel tubes / passive bundle X 5 blanket rods / fuel tube

= 756,160 blanket rods.

Hence the total number of blanket rods is:

1,012,928 blanket rods + 756,160 blanket rods = **1,769,088 blanket rods**

The fuel mass of each reactor is significant. The major fuel mass components consist of:

Core fuel rod mass = 253,232 core fuel rods X 0.28725 kg / core rod = 72,740.892 kg=

=

This web page last updated December 27, 2017

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