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**INTRODUCTION:**

This web page deals with FNR fuel rods.

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 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 nominally 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 556 active fuel tubes / active bundle X 1 core rod / active fuel tube = **295,792 core fuel rods**

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

532 active bundles X 556 active tubes / active bundle X 4 blanket rods / active tube = 1,183,168 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:

1,183,168 blanket rods + 756,160 blanket rods = **1,939,328 blanket rods**

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

Core fuel rod mass = 295,792 core fuel rods X 0.28725 kg / core rod = 84,966.252 kg=

=

This web page last updated January 13, 2017

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