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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 keep both fuel and fission products from mixing with the primary liquid sodium. The material properties of the FNR fuel tubes dictate many aspects of FNR design. One constraining issue is the tolerable level of stress in the fuel tube wall which normally operates at 330 to 460 degrees C in an intense fast neutron flux.

At the bottom of each fuel tube is a bottom plug.

Active fuel tubes contain 4 X 0.600 m long X 8.93 mm diameter blanket rods initially consisting of 90% uranium and 10% zirconium and 1 X 0.35 m long X 8.08 mm diameter core rod initially consisting of 70% uranium-20% plutonium-actinide-10% zirconium alloy.

Passive fuel tubes contain 5 X 0.600 m long X 8.93 mm diameter blanket rods initially consisting of 90% uranium and 10% zirconium.

The fuel tubes contai enough liquid sodium to provide good thermal contact between the fuel rods and the fuel tube throughout the working life of the fuel tube.

The fuel tube must have a sufficient wall thickness to safely withstand repeated internal liquid sodium freezing and remelting.

The top of the fuel tube is closed with a top plug.

The internal pressure stress is limited by provision of a plenum for each fuel tube. The plenum has sufficient volume to store at a reasonable pressure the inert gas fission products that accumulate during a fuel cycle.

During a fuel cycle due to fast neutron irradiation the fuel tube alloy significantly changes, which changes its basic 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 internal inert gas pressure DeltaP rises.

The choice of alloy for use in a Fast Neutron Reactor (FNR) fuel tubes is critical. A major issue with Austenitic stainless steel such as 316 used at 420 C is that under prolonged fast neutron exposure it swells as much as 25% whereas under the same neutron exposure ferritic steels expand < 1%. This swelling will reduce the flow of cooling primary liquid sodium through the reactor core.

It is shown on the web page FNR FUEL TUBE WEAR that to minimize fuel tube material swelling a good fuel tube material is the alloy HT-9. HT-9 contains 12% chromium which for T < 460 C keeps HT-9 in the alpha + alpha prime phase with a BCC lattice. HT-9 remains in the alpha + alpha prime phase as due to fast neutron impacts the Fe fraction decreases and the Cr fraction increases. The chromium also has a BCC lattice. HT-9 contains almost no nickel.

A complicating issue with Fe - Cr alloys is a phase change out of BCC that occurs in the temperature range 460 degrees C to 512 degrees C. This phase change will cause fuel tube material swelling and will severely weaken the alloy. To avoid this phase change the maximum primary liquid sodium working temperature in a FNR is set at 450 degrees C. In a practical FNR about 4.5 m of each active fuel tube operates at 450 degrees C. Subject to liquid sodium circulation and steam temperature constraints it may be desirable to further lower this working temperature to ensure long fuel tube working life.
 

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.

Then the corresponding internal pressure in the tube is:
DeltaP = [(Ro - Ri) / Ri] Sh
= [(0.065 inch) / (0.500 inch)] 68.7 MPa
= 8.931 MPa
This is the maximum allowable gas pressure inside the tube.
 

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
and
Ta ~ (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 yield stress Sy.
 

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.

Thus 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 fast neutron irradiated HT-9 operated below 425 degrees C becomes extremely brittle.
 

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 GPa211 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

 

FUEL TUBE MATERIAL:
The optimum choice of fuel tube material for an FNR is a complex issue. The choice of fuel tube material and the working life of that material are addressed on the web page titled: FNR FUEL TUBE WEAR. 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 330 degrees C and the temperature at the top of the primary liquid sodium pool is about 450 degrees C. Various parts of a fuel tube operate in the temperature range 330 C to 460 C. In this temperature range HT-9 is subject to fast neutron induced embrittlement. Hence an issue in fuel bundle design is provision for fast neutron induced fuel tube embrittlement. The fuel tubes must also safely accommodate fuel bundle insertion into the FNR primary liquid sodium pool while the sodium inside the fuel tube 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. The most common nickel isotope, Ni-58, promotes (n, alpha) reactions that yield He-4, which causes fuel tube material swelling. 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 453,456 fuel tubes that must be automatically fully fabricated, assembled, and tested.

Note that the seal of the fuel tube top plug, which contains inert gas at 450 C, may be more critical than the seal of the bottom plug, which contains liquid sodium at 330 C. Hence the top plug is applied 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.

The fuel tube alloy must be chemically compatible with Na, UO2, U, Pu, Zr, fission products, transuranium actinides from 20 degrees C to 500 degrees C.
 

SOLID SODIUM INSIDE FUEL TUBE:
As shown at FNR Design in order to withstand local melting of sodium inside the fuel tube the fuel tube wall thickness should be about 0.065 inch for a 0.500 inch OD HT-9 fuel tube.
 

THERMAL WALL STRESS:
Due to the radial heat transport the inside of a core fuel tube wall is under compression. The outside of a core tube wall is under tension.

Recall that:
Stc = Y (TCE) (Ti - To) / 2
or
(Ti - To) = 2 Stc / [Y (TCE)]

For the special case of zero internal gas pressure stress the theoretical maximum wall temperature differential DeltaT is given by:
(DeltaT) = (Sy)(2) / [(TCE) Y]
 

If there is fuel tube material creep these stresses will cause the fuel tube diameter to gradually increase.

FOR HT-9 FUEL TUBES:
The maximum differential temperature across the fuel tube wall is:
(DeltaT)
= (Sy)(2) / [(TCE) Y]
= [(450 X 10^6 Pa)(2)] / [ (15.0 X 10^-6 / deg C) X (2000 X 10^9 Pa)]
= [900 X 10^6 deg C] / [30.0 X 10^6 ]
= 30.0 deg C

For a conservative safe design the maximum material thermal stress and hence the maximum operating temperature differential across the fuel tube wall should be reduced by a factor of two to: 15.0 deg C. Note that this design safety factor should allow modest fuel thermal power transients without cracking the fuel tubes.

The corresponding operating value of Stc is:
(450 X 10^6 Pa ) / 2 = 225 MPa.

The corresponding value of (Sh + Stc) is:
68.7 MPa + 225 MPa = 293.7 MPa
which is less than (0.75 Sy) and is prudent as long as there is experimental evidence that Sy > 400 MPa.

Thus the maximum safe continuous operating heat flux through the HT-9 steel tubes of the reactor core is:
15.0 deg C X 26.2 W / m-deg C / (.065 inch X .0254 m / inch) = 238,037 W / m^2

The core tube external surface area is:
Pi X (.500 inch) X (.0254 m / inch) X 0.35 m / tube X 556 active tubes / bundle X 532 active bundles = 4130.5 m^2

Hence the corresponding maximum allowable reactor thermal power is:
238,037 W / m^2 X 4130.5 m^2 = 983,211,828 Wt
= 983.2 MWt

It is necessary to rely on the gas plenum volume to prevent excessive inert gas pressure buildup in the fuel tube.
 

FUEL TUBE SWELLING:
A key issue in making a Fast Neutron Reactor (FNR) economic is to minimize the problem of fuel tube swelling. A fuel tube outside diameter (OD) increase reduces the external cross sectional area for liquid sodium coolant flow, which effectively limits reactor power output and hence limits the fuel tube working life. The methodology contemplated herein is to use a swelling resistant fuel tube material and to use a square tube lattice.

The fuel tube is initially 0.500 inch OD, 0.37 inch ID. The end plugs, after being cooled with liquid nitrogen, are slid into the fuel tube. As the end plugs warm up their OD makes a gas tight seal to the fuel tube ID and are welded in place. 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 grid.

Core fuel rod material and blanket fuel rod material are transported in rod form. Fuel tubes and fuel bundles are assembled and disassembled at FNR sites. Thus sodium-air and sodium-water chemical reactions that might occur as a result of transportation accidents are avoided.

As the outside diameter of the fuel tubes swells the cross sectional area available for external liquid sodium coolant flow decreases. This fuel tube swelling problem in a FNR is challenging because in a FNR one of the design objectives is to burn the fuel as long as possible to minimize the required amount of fuel reprocessing.

Experimentally with 316L fuel tubes at 510 degrees C fuel tube volume increases of 33% have been observed at a fast neutron exposure of 80 dpa (displacements per atom). With the fuel tube material HT-9 the corresponding fuel tube volume increase appears to be about 4%. However, the tube material HT-9 has temperature and neutron irradiation related embrittlement issues.

It is helpful to understand the fuel tube swelling problem both in terms of fuel tube centre-to-centre geometry and in terms of the underlying causes of fuel tube swelling.

The increase in fuel tube diameter is caused by a combination of phenomena including:
a) Swelling of the fuel tube material caused by helium gas formation withing the fuel tube material lattice;
b) Swelling of the fuel tube material due to the high thermal flux and high temperature causing material creep;
c) Swelling of the fuel rod inside the fuel tube due to formation of internal gas bubbles within the fuel rod;
d) Swelling of the fuel rod inside the fuel tube due to formation of two atoms in place of one during the fission process;
e) An increase in fuel tube internal pressure caused by differential thermal expansion of the contained liquid sodium as compared to the fuel tube material;
f) An increase in fuel tube internal pressure due to formation and trapping of of inert gas fission products;

These problems are aggravated by a decrease in fuel tube wall yield stress due to low nickel content, high operating temperature, fast neutron flux disruption of the fuel tube atomic constituants and spontaneous changes in fuel tube lattice from BCC to HCP as chromium converts to titanium once Ti is no longer held by Fe2Ti.

The solutions to this fuel tube swelling problem include:
1) Use a square tube lattice instead of a hexagonal tube lattice so that the tube swelling has reduced impact on the external primary liquid sodium coolant flow;
2) Use of a fuel tube material that maintains a sufficient yield stress at 450 C under fast neutron irradiation so that it resists diameter expansion due to thermal and internal gas pressure stress;
3) Use of a fuel tube material with a relatively small Youngs modulus (modulus of elasticity) to minimize thermal stress in the tube material;
4) Use of a fuel tube material with a relatively high thermal conductivity to minimize thermal stress in the tube material;
5) Use of core fuel rod and blanket fuel rod ODs that are sufficiently small with respect to the fuel tube ID that mechanisms (c) and (d) have no effect on fuel tube hoop stress;
6) Use of a fuel tube steel wall that is sufficiently thick with respect to its ID that the fuel tube can withstand the differential thermal expansion of sodium as compared to the fuel tube material below the melting point of sodium;
7) Use of a large gas plenum at the top of the fuel tube to limit the inert gas pressure inside the fuel tube;
8) Provide sufficient additional plenum volume to allow for differential thermal expansion of liquid sodium;
9) Provide sufficient additonal plenum volume to allow for extra sodium that is required as the fuel tube material swells in both diameter;
10) Provide sufficient additonal plenum volume to allow for extra sodium that is required as the fuel rod material swells in length;
11) Provide sufficient sodium to chemically absorb the fission products bromine and iodine.

The aforementioned fuel tube design keeps the maximum fuel tube material stress safely below the fuel tube material yield stress at all projected operating temperatures.
 

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

FUEL TUBES ON STAGGERED CENTRES:
Consider fuel tubes that are initially 0.500 inch OD located on 0.625 inch staggered centres. Viewed from the bottom or top of the reactor for each fuel tube there are two associated equilateral triangles with sides of length 0.625 inch. The height of such a triangle is:
(3^0.5 / 2)(.625 inch)

The area of the triangle is:
(1 / 2)(.625 inch)(3^0.5 / 2)(.625 inch) = (3^0.5 / 4)(.625 inch)^2
= 0.16914 inch^2

The two triangles together form a rhombus of area:
2 (.16914 inch^2) = 0.33828 inch^2

The initial cross sectional area of the fuel tube is:
Pi (.25 inch)^2 = .19634 inch^2

Thus the initial cross sectional area available for liquid sodium flow is:
0.33828 inch^2 - 0.19634 inch^2 = 0.14194 inch^2

Now assume that the fuel tube expands from 0.500 inch OD to 0.625 inch OD. Its cross sectional area increases to:
Pi (.625 inch / 2)^2 = 0.30679 inch^2

Hence the cross sectional area available for liquid sodium flow falls to:
0.33828 inch^2 - 0.30679 inch^2 = .03149 inch^2

Thus the fractional liquid sodium flow area remaining is:
.03149 inch^2 / 0.14194 inch^2 = 0.22185
 

FUEL TUBES ON SQUARE CENTRES:
Consider fuel tubes that are initially 0.500 inch OD on 0.625 inch square centres. Viewed from the bottom or top of the reactor for each fuel tube there is a square with sides of length 0.625 inch. The height of such a triangle is:
0.625 inch.

The area of the square is:
(.625 inch)^2
= 0.390625 inch^2

The initial cross sectional area of the fuel tube is:
Pi (.25 inch)^2 = .19634 inch^2

Thus the initial cross sectional area available for liquid sodium flow is:
0.390625 inch^2 - 0.19634 inch^2 = 0.194285 inch^2

Now assume that the fuel tube expands from 0.500 inch OD to 0.625 inch OD. Its cross sectional area increases to:
Pi (.625 inch / 2)^2 = 0.30679 inch^2

Hence the cross sectional area available for liquid sodium flow falls to:
0.390625 inch^2 - 0.30679 inch^2 = .083835 inch^2

Thus the fractional liquid sodium flow area remaining is:
.083835 inch^2 / 0.194285 inch^2 = 0.431505

Thus in terms of liquid sodium coolant flow a square lattice tube geometry is twice as good as a staggered lattice tube geometry. Hence the tube bundles should be square instead of hexagonal. In plan view the reactor should be octagonal instead of hexagonal.
 

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

The gas pressure in the fuel tube plenum is caused by fission products that are gaseous at 450 degrees C.
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 tha above table we must be concerned about anything that has a melting point between 280 C and 550 C because if such materials leak into the primary liquid sodium they will deposit on the 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%
 

Core rod mass = 0.28725 kg _________

The mass converted to fission products in total plutonium-uranium burnup in an active fuel tube is:
(initial active fuel tube uranium-plutonium weight)
= (0.9 X 0.28725 kg)

Let Fb = fuel burnup fraction in one fuel cycle

Core rod mass converted to fission products in one fuel cycle is:
Fb (0.9 X 0.28725 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 (0.9 X 0.28725 kg) 5.746 X 10^-2

_______

The atomic weight of krypton is: 83.798

The number of moles of krypton produced is:
[ Fb (0.9 X 0.28725 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 (0.9 X 0.28725 kg) (8.799 X 10^-2)

The atomic weight of xenon is: 131.293

The number of moles of xenon produced is:
[Fb (0.9 X 0.28725 kg) (8.799 X 10^-2) X 1000 g / kg] / [131.293 g / mole]

The total number of moles of inert gas produced in one fuel cycle is:
[ Fb (0.9 X 0.28725 kg) (5.746 X 10^-2) X 1000g / kg] / [83.798 g / mole]
+ [Fb (0.9 X 0.28725 kg) (8.799 X 10^-2) X 1000 g / kg] / [131.293 g / mole]
= [Fb (0.9 X 0.28725) [(57.46 / 83.798) + (87.99 / 131.293)] moles
= [Fb (0.9 X 0.28725) [(0.6857) + (0.6702)] moles
= 0.3505 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 450 deg C = 723 deg K and at the above calculated maximum pressure of 8.931 MPa occupies a volume of:
(22.4 X 10^-3 m^3 / mole) X (723 K / 273 K) X (0.101 MPa / 8.931 MPa)
= 0.67088 X 10^-3 m^3 / mole

Hence the minimum required plenum volume for storage of inert gas fission products at 450 C and 8.931 MPa is:
(0.67088 X 10^-3 m^3 / mole) X (0.3505 Fb) moles inert gas)
= (0.2351 Fb) X 10^-3 m^3

The inside cross sectional area of the fuel tube is given by:
Pi (0.37 inch / 2)^2 X (.0254 m / inch)^2
= 0.69368 X 10^-4 m^2

Hence the minimum dedicated plenum length required for inert gas storage is:
[(0.2351 Fb) X 10^-3 m^3] / 0.69368 X 10^-4 m^2]
= 3.389 Fb m
 

PLENUM VOLUME REQUIRED TO ACCOMMODATE LIQUID SODIUM:
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.

Each fuel tube has a plenum to provide volume for inert gas storage, for liquid sodium storage and to provide allowance for differential liquid sodium thermal expansion. The dedicated gas portion of the plenum limits the internal pressure in the fuel tube as the fuel rods release inert gas fission products.

From the web page titled FNR DESIGN the initial diameters of the fuel rods are:
Core Rod = 8.08 mm
and
Blanket Rod = 8.93 mm

The minimum volume of liquid sodium initially required inside a fuel tube to immerse the fuel rods is:
Pi [(.37 inch / 2)^2] [0.0254 m / inch]^2 [2.75 m] - Pi[(4.04 X 10^-3 m)^2 (0.35 m)] - Pi [(4.465 X 10^-3 m)^2 (2.4 m)]
= Pi [0.60721653 X 10^-4 m^3 - 0.0571256 X 10^-4 m^3 - 0.4784694 X 10^-4 m^3]
= 0.22500 X 10^-4 m^3

The additional volume of liquid sodium required to accommodate a 10% increase in fuel tube diameter over a length of 2.8 m is:
[(1.1)^2 - 1] Pi [(.37 inch / 2)^2] [0.0254 m / inch]^2 [2.8 m]
= .407885 X 10^-4 m^3

The maximum volumetric thermal expansion of the liquid sodium is:
271 X 10^-6 / C X 350 C X (0.22500 + .407885) X 10^-4 m^3
= .060694 X 10^-4 m^3

The core rod swelling will occur long before fuel tube swelling occurs, thus forcing surrounding liquid sodium into the plenum. The volume of that liquid sodium is:
Pi [(.37 inch / 2)^2] [0.0254 m / inch]^2 [.35 m] - Pi [(4.04 X 10^-3 m)^2] [0.35 m]
= Pi [.077282 X 10^-4 m^2 - 0.0571256 X 10^-4 m^3]
= 0.063323 X 10^-4 m^3

The liquid sodium that the fuel tube plenum must accommodate is:
(.407885 X 10^-4 m^3) + (0.060694 X 10^-4 m^3) + (0.063323 X 10^-4 m^3)
= 0.5319 X 10^-4 m^3

The fuel tube inside cross sectional area is:
Pi (0.37 inch / 2)^2 (0.0254 m / inch)^2
= 6.93681953 X 10^-5 m^2

Hence the minimum plenum height dedicated to liquid sodium should be:
(.5319 X 10^-4 m^3) / (6.93681953 X 10^-5 m^2)
= 0.7667 m

When the liquid sodium is just above its melting point and before any material swelling has occurred the height of liquid sodium in the plenum is:
(.407885 X 10^-4 m^3) / (6.93681953 X 10^-5 m^2)
= 0.5879 m
 

TOTAL PLENUM REQUIREMENT:
Hence the minimum total plenum height is:
(inert gas height) + (sodium height)
= 3.389 Fb m + 0.7667 m
where Fb is the fuel burn-up fraction

Thus a 3.0 m high plenum is sufficient to ensure that plenum gas pressure will not be a constraining issue on the power FNR. The burnup fraction will likely be limited by accumulation of neutron absorbing fission products. Another reason for retaining the tall plenum is to enhance natural circulation of primary liquid sodium.

Thus fuel tube swelling, core rod swelling, liquid sodium thermal expansion and inert gas accumulation all make significant demands on the available plenum volume.
 

This web page last updated January 13, 2017

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