# XYLENE POWER LTD.

## FNR TEMPERATURE SETPOINT

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

FNR TEMPERATURE SETPOINT:
This web page is primarily concerned with the change in FNR fuel geometry necessary to maintain the desired FNR temperature setpoint To as the core fuel ages.

A FNR differs from water cooled reactors in that in a FNR the reactivity is a function of FNR average fuel temperature.

Let the number of free neutrons in the reactor core zone by N. The fuel geometry of a FNR is chosen such that at the desired operating temperature:
T = To
dN / dt = 0

dN / dt = N [M Sigma V - k]
where: M = concentration of fissile atoms which is a function of temperature T.

Thus at temperature To:
[M Sigma V - k] = 0

M decreases with increasing temperature.

When the FNR average fuel temperature T is above setpoint To then:
[M Sigma V - k] < 0
and the concentration of free neutrons N in the reactor core zone decays with increasing time reducing the fission thermal power output.

If T < To then:
[M Sigma V - k] > 0
and the concentration of free neutrons N in the reactor core zone grows with time which increases the fission thermal power output.

The system converges to a steady state condition where the fission thermal power output equals the rate at which heat is removed by the coolant and T = To.
We need to investigate the stability of this solution.

Due to neutron diffusion the fission heat is distributed over the nearby nuclear core fuel volume.

Setpoint temperature To is a function of the fuel geometry. At T = To:
[M Sigma V - k] = 0
which gives:
dN / dt = 0
corresponding to constant thermal power.

The setpoint temperature To is stable as long as the fuel geometry is stable. The setpoint temperature To can be changed by changing the fuel assembly geometry.

Let Tpi be the primary coolant inlet temperature to the fuel assembly. As long as:
Tpi < To
the average fuel temperature remains at temperature To.

A FNR can easily be damaged if the quantity:
(To - Tpi)
becomes too large, which can happen if either To is raised too quickly or if the FNR is thermally over loaded so that the primary sodium coolant inlet temperature Tpi to the fuel assembly drops too low.

To sufficiently protect a FNR against damage it is necessary to recognize that the flow of primary liquid sodium coolant through a fuel bundle may not be uniform due to the fuel tubes not being absolutely straight, due to fuel bundle non-uniformity and due to potential long term obstruction of coolant channels by suspended particulate matter. An isolated obstructed coolant channel causes a 25% reduction in the cooling available for each of the four adjacent fuel tubes. Hence the temperature rise along each of these four adjacent fuel tubes is about 33% larger than for the other fuel tubes in the same fuel bundle. Hence if the nominal coolant temperature rise along the fuel tube is 100 degrees C a few fuel tubes will experience temperature rise of 133 degrees C. Since all the coolant channels share the same coolant inlet temperature Tip, the extra 33 degrees C is added on to the local discharge temperature Tdp.

Note that the fuel geometry is affected by both thermal expansion of the fuel and by thermal expansion of the fuel bundle. Both mechanisms affect the average concentration of fissionable atoms in the reactor core region but only the fuel temperature can respond to changes in fission power at the rate necessary to suppress a prompt critical condition.

The physics of FNR thermal power control are discussed later herein but for now we need to consider the control system's important practical implications.

Consider a round fuel rod. If the presence of a coolant reduces the temperature of the outer surface of the fuel rod below To then the temperature of the fuel rod centerline will go above To in order to keep the average fuel temperature at To.

As shown at FNR Fuel Rods at full load when the fuel center line temperature maximum is 560 deg C the primary liquid sodium discharge temperature Tdp|max is about:
560 - 53.11 - 8 - (sodium boundary layer temperature drop) = 495 degrees C.

Now allow for the 33 degees C due to isolated obstructed coolant channels.Then:
Tpd|max = 495 - 33 = 462 degrees

Assume that the fuel assembly is designed so that at full load the normal temperature rise:
(Tpd - Tpi) = 100 degrees C
Hence at full load the fuel rod centerline temperature Tc at its cool end is Tcc which is 50 degrees C below average centerline temperature Tca, or
Tcc = Tca - 50 C
and at the fuel rod hot end Tc will rise to
Tch = Tca + 50 degrees C,
provided that the ends are not so far apart as to not share fission neutrons. This phenomena enables a relatively uniform heat production in the fuel rod and smooth coolant temperature rise along the length of the fuel rod. Thus, if at full load the primary coolant inlet temperature is
Tpi = Tpd - 100 degrees C
and the primary coolant discharge temperature is
Tpd
and the full load differential temperature between the fuel rod center line and the coolant is 65 degrees C the fuel rod centerline temperature may vary from the cool end:
Tcc = (Tpd - 100 + 65)
to the hot end
Tch = (Tpd + 65)
with an average full load fuel center line temperature:
Tca = [(Tpd - 100 + 65) + (Tpd + 65)]/ 2
= Tpd + 65 -50
= Tpd + 15 deg C

Tca = To + (53 / 2) C
which gives:
(To + 26.5 C) ~ (Tpd + 15 C)
or
Tpd = To + 11.5 C

Tpd ~ To

Note that as the FNR coolant inlet temperature Tpi falls the FNR coolant discharge temperature Tpd rises. This issue can potentially lead to centerline fuel melting at the hot end of the core fuel rod stack if the coolant is too cold.

A matter of serious concern is the fuel center line temperature at its hot end which, if an isolated cooling channel is obstructed, can potentially exceed the material rating.

Tch = Tpd + 65 C + 33 C
= To + 11.5 C + 98 C
= To + 109.5 C

Since Tch|max = 560 C,
To = (560 C - 109.5 C) = 450.5 C

Thus, when the reactor is not loaded the sodium surface temperature should be about 450.5 C so that when the reactor is heavily loaded the sodium surface temperature rises to 462 C to keep the worst case fuel centerline temperature less than 560 C.

Note that the moveable fuel bundles must be very slowly inserted in no load conditions to ensure that:
To - Tpi < 100 C

Recall that at maximum FNR load:
Tpd = To + 11.5 C
or
To = Tpd - 11.5 C

Hence:
Tpd - Tpi < 100 C
requires that:
To + 11.5 C - Tpi < 100 C
or
(To - Tpi) < 88.5 C

In summary, during FNR warmup it is important to very slowly increase To so that at all times:
(To - Tpi) < 88.5 C

It is easy to damage a FNR during warm up by increasing To so fast that:
(To - Tpi)
exceeds 88.5 degrees C.

Like other nuclear reactors a FNR normally operates such that when the primary coolant inlet temperature Tpi is less than the FNR setpoint temperature To the rate of free neutron generation exactly equals the rate of free neutron loss. If the primary coolant inlet temperature Tpi decreases the reactor thermal power increases and if the primary coolant inlet temperature Tpi decreases the reactor power increases.

The thermal resistance related to the fuel tubes in a FNR causes the FNR coolant discharge temperature Tpd to be less than the temperature Tch which is the fuel rod center line temperature at the hot end of the fuel rod. The temperature difference:
(Tch - Tpd)
is almost proportional to the reactor thermal power and in a practical FNR varies linearly from about 0 degrees C to about 65 degrees C at maximum plate rated reactor thermal power. This thermal resistance R is the combined effect of the finite thermal conductivities of the fuel alloy, the sodium internal to the fuel tubes, the fuel tube wall and the sodium coolant boundary layer on the outside of the fuel tube wall.

Thus we have the equation:
(Tch - Tpd) = P R
where:
P = reactor thermal power
and
R = the FNR internal thermal resistance.

P = 1000 MWt
(Tch - Tpd) = 65 deg C
then:
R = (Tch - Tpd) / P
= [65 deg C / Pmax]
wher Pmax = maximum rated power.

Rearranging this equation gives:
Tpd = (Tch - P R)

However, the reactor thermal power P can also be expressed in terms of the coolant temperature rise in the form:
P = Fp Cp (Tpd - Tpi)
where:
Fp = primary coolant mass flow rate;
and
Cp = coolant heat capacity.

Hence:
P = Fp Cp (Tpd - Tpi)
= Fp Cp (Tch - P R - Tpi)

Rearranging this equation gives:
P [1 + Fp Cp R] = [Fp Cp (Tch - Tpi)]
or
P = [Fp Cp (Tch - Tpi)] / [1 + Fp Cp R]

The import of this equation is that if there is a high primary coolant flow rate Fp, the temperature differential:
(Tpd - Tpi)
may have to be reduced to prevent the FNR's thermal power rating being exceeded.

In the contemplated FNR conservation of energy at the intermediate heat exchanger causes:
Fp (Tpd - Tpi) = Fs (Tsd - Tsi)
or
Fp = Fs (Tsd - Tsi) / (Tpd - Tpi)

However due to counter current intermediate heat exchange design:
Tpd ~ Tsd + 10 C
Tpi ~ Tsi + 10 C
which gives:
(Tpd - Tpi) ~ (Tsd - Tsi)
and
Fp ~ Fs

For a FNR which relies on natural primary sodium circulation this relationship indirectly sets the required number of active fuel tubes corresponding to a particular secondary sodium flow rate.

Note that as primary coolant flow rate Fp goes to zero then P goes to zero.

In the practical FNR described herein Fs is controlled to limit the FNR thermal power.

In the envisaged FNR in order to have sufficient primary sodium natural circulation we want to operate at:
P = 1000 MWt at:
Tdp = 440 to 472 C,
Tip = 340 C

Recall that:
P [1 + Fp Cp R] = [Fp Cp (Tch - Tpi)]
or
F Cp [(Tch - Tpi) - (P R)] = P
or
F = P / Cp [(Tch - Tpi) - (P R)]
= P / Cp [Tpd - Tpi]
= 1000 MWt / Cp [100 deg C]

Thus the key to FNR durability is to limit the reactor power by limiting both the maximum coolant flow rate Fp and the maximum possible temperature differential:
(Tpd - Tpi).

For a reactor intended to operate with:
(Tpd - Tpi) = 100 degrees C
it is important on reactor startup to slowly raise the fuel temperature setpoint To to gradually raise the temperature Tip in the sodium pool so that the difference between Tpd and Tpi never exceeds 100 degrees C.

SIMPLE SUMMARY WARNING:
Historically in other liquid sodium cooled reactors there have been a number of cases of FNR fuel tube melting. It is important to realize that the nuclear reaction will deliver the instantaneous thermal power:
P = F Cp (Tpd - Tpi)

The nuclear reaction is completely unaware that the product:
Fp Cp (Tpd - Tpi)
can easily physically exceed the FNR's fuel tube heat transport capacity, thus causing a fuel tube failure.

It is up to the FNR system designer to do all necessary to keep the product:
Fp Cp (Tpd - Tpi)
within the FNR physical material limits. Historically previous FNR designers often used a pump to fix coolant flow rate Fp. The use of such a pump reduces thermal stress. However, that pump immediately imposes significant serious constraints on the safe range of (Tpd - Tpi).

In simple language the nuclear reaction in a FNR supplies sufficient instantaneous thermal power to maintain the FNR average fuel temperature at To, irrespective of FNR material related heat transport limitations. If the system designer fails to do all necessary to limit the maximum value of:
Fp Cp (Tpd - Tpi)
or if operators defeat mechanisms designed to limit the rate of change of To sooner or later the fuel tube heat transport capacity will be exceeded and the fuel tubes will be damaged.

The effect of changing the reactor fuel geometry is to change To. The To setting is NEVER adjusted during normal reactor operation. To is only reduced when it is necessary to lower the temperature of the primary sodium pool, as might be required during reactor refueling or when replacing an intermediate heat exchange bundle. During subsequent reactor warmup To is very slowly increased so that (Tpd - Tpi) always remains less than 100 degrees C and for the same reason the primary sodium pool heat output is kept at minimum during the primary sodium pool warm up to limit the temperature difference:
(Tpd - Tpi)

Suppose that there was a historical FNR that for some reason was shut down using its control rods and the sodium coolant pump was shut off. While in the off state the sodium pool gradually cooled. When the reactor was to be used again the control rods should have been very slowly withdrawn to gradually bring the sodium pool back to design operating temperature BEFORE the coolant pump was turned on. Turning the coolant pump back on before the sodium pool reaches design operating temperature would cause a FNR thermal power surge likely sufficient to damage the fuel tubes.

OPERATING SUMMARY:
The FNR thermal power is proportional to both the coolant flow rate Fp and
(Tpd - Tpi).
As long as Tpi < To the fuel temperature To in a FNR remains constant. A FNR spontaneously varies its thermal power output to maintain a constant average fuel temperature To. In normal electricity generation applications setpoint To is kept constant and flow rate Fp is varied. Flow rate Fp is a natural circulation flow rate. However, due to the use a counter current heat exchange arrangement, Fp follows the secondary sodium flow rate Fs, which is mainly established by induction pumps. In the event of loss of station power the induction pumps will not operate, but the FNR secondary sodium system is designed to provide enough secondary sodium natural circulation to remove fission product decay heat.

The advantages of setting To and varying Fs include:
a) System safety;
b) Avoiding any need for primary sodium circulation pumps.

The advantage of fixing Fp and varying To as has been done by others is a lower value of (Tpd - Tpi) and hence less thermal stress on the fuel assembly and intermediate heat exchange bumdles as the FNR changes its operating power level.

FNR PHYSICS:
A FNR core zone, where the fixed and movable fuel bundles overlap, produces an excess of neutrons which diffuse out of the core zone and into the adjacent blanket zones. The blanket zones net absorb neutrons. When the core fuel is new about half of the fission neutrons generated in the core zone diffuse into the blanket zones. As the core fuel ages the thickness of the core zone is gradually increased and the fraction of fission neutrons that diffuse from the core zone into the blanket zones gradually decreases. When this fraction approaches zero it is no longer possible to maintain reactor power control at the desired reactor temperature setpoint To so the core fuel must be replaced.

Typically core fuel replacement is required after 15% of core fuel mass has become fission products.

FNR BASIC CRITICALITY REQUIREMENTS:
1) When the movable active fuel bundles are fully inserted in the matrix of fixed active fuel bundles and the core fuel is nearly fully depleted (average 12.7% Pu) the reactor must still be critical. This is the depleted fuel condition.

2) When the movable fuel bundles are 1.2 m withdrawn and the core fuel is new (average 20% Pu) the reactor must be reliably sub-critical. This is the new fuel cool____ shutdown condition. In this condition the mobile active fuel bundles form a lower core fuel layer and the fixed active fuel bundles form an upper core fuel layer. The two layers are separated by 0.5 m of blanket rod material. Both the upper core fuel layer and the lower core fuel layer must each be individually subcritical.

This requirement for subcriticality in the upper and lower core fuel zones limits the maximum Pu-239 concentrations and hence weight fractions in the core fuel rods.

PROTECTION AGAINST A DEFECTIVE CONTROL SYSTEM:
In the event that due to a control system malfunction a new movable fuel bundle is erroneously driven toward its fully inserted state it is essential for the other movable fuel bundles, which are separately controlled, to immediately fully withdraw to cause a reactor cool shutdown.

When the fuel is new (average 20% Pu) and every second movable active fuel bundle is at its normal insertion depth while the remaining movable active fuel bundles are fully withdrawn the chain reaction must stop. This condition ensures that a cool shutdown condition is attainable with any one movable fuel bundle jammed in its normal operating position.

It is important to ensure that one isolated movable active fuel bundle with new fuel will not go prompt critical if it is accidentally fully inserted into the octagonal bundle matrix. As this circumstance is occurring the other independent shutdown system must instantly force a reactor cool shutdown. That cool shutdown will cause the four nearest neighbour movable fuel bundles to immediately fully withdraw. Hence, in all fuel conditions reactor prompt neutron criticality must be impossible if the four nearest neighbour movable active fuel bundles are fully withdrawn.

For clarity if the fixed fuel bundles are designated by F and the interlaced movable fuel bundles are grouped by A, B then in plan view:
ROWFUEL BUNDLE TYPE
1 F A F A F A F A F A F A F A F A F A
2 B F B F B F B F B F B F B F B F B F
3 F A F A F A F A F A F A F A F A F A
4 B F B F B F B F B F B F B F B F B F

Note that each fixed fuel bundle F is surrounded by 2 X A and 2 X B with 4 fixed bundles on diagonals (except for the outer perimeter).
Note that each type A movable bundle is surrounded by 4 X F fixed bundles with 4 X B movable bundles on diagonals (except for the outer perimeter);
Note that each type B movable bundle is surrounded by 4 X F fixed bundles with 4 X A movable bundles on diagonals (except for the outer perimeter).

Note that A and B bundles occur in every second row and every second column.

Thus if any A bundle jams the four nearest B bundles are withdrawn to compensate. Similarly if any B bundle jams the four nearest A bundles are withdrawn to compensate.

Achieving certain reactor shutdown while allowing for the desired range of Pu-239 concentration decay in the core fuel rods likely requires a 1.2 m control portion withdrawal. A 1.8 m blanket thickness is required to guarantee 1.1 m blanket thickness at times when there is almost no overlap between the fixed and movable core fuel rods. More typically the fuel bundle core rod overlap is 0.35 m resulting in a guaranteed 1.45 m blanket thickness.

FUEL BUNDLE STATE DIAGRAM:
The insertion positions for a line of 8 movable fuel bundles inserted between 9 fixed fuel bundles are shown below for the cases of reactor cool shutdown, normal reactor operation and reactor at maximum possible power. In the reactor cool shutdown state the core rods (red) form two widely separated upper and lower core rod fuel concentration layers. In the normal reactor operating state the fixed and movable core rods partially overlap forming the core zone. As the fuel ages the amount of core rod overlap is gradually increased which increases the thickness of the core zone. When the fixed and movable core rods fully overlap the fuel bundles are ready to be removed for cooling and then reprocessing.

Reactor Cool Shutdown

Normal Reactor Operation

Reactor at Maximum Movable Fuel Bundle Insertion

Note that the maximum permitted vertical travel of a movable fuel bundle is 1.2 m which causes the transition between the movable fuel bundles fully withdrawn (reactor cool______ shut down) and movable fuel bundles fully inserted (maximum power) states. Note that over insertion of the movable fuel bundles into the matrix of fixed fuel bundles could potentilly cause prompt neutron criticality.

PROMPT NEUTRON CRITICALITY SUPPRESSION:
Note that in normal operation the reacting end of the core fuel rod stack is hotter than the opposite end. If the hot end of a core fuel rod stack rapidly gets too hot it will vaporize the fission product Cs and then vaporize the adjacent liquid Na contained inside the fuel tube. In the movable fuel bundles the vapor pressure tends to blow the upper blanket rods into the plenum while holding the core fuel rods in place. In the fixed fuel bundles the vapor pressure tends to blow both the core fuel rods and the upper blanket rods into the plenum. This action, which happens in a fraction of a ms time frame, separates the fixed fuel bundle core fuel rods from the movable fuel bundle core fuel rods, which reduces the reactor reactivity and will suppress a prompt critical condition.

Note that absent core fuel rod cool end beading, due to vapor leaking past the core fuel rods the aforementioned prompt criticality suppression mechanism might not operate reliably until the core fuel rods in the fixed fuel bundles have swelled enough to fill the fuel tube. That swelling relies on formation of inert gas bubbles in the fuel which may take weeks to fully form. Until the core fuel rods in the fixed fuel bundles have swelled enough to fully fill the fuel tube fuel rod sodium trapping and end beading are relied upon to suppress a prompt critical condition.

CORE ZONE REACTIVITY OVERVIEW:
The function of the FNR core is to maintain a nuclear chain reaction via fissioning of Pu-239, Pu-240 and other transuranium actinides while emitting surplus neutrons to the FNR blanket. A fundamental question from a practical reactor engineering perspective is: "What is the proper range of core zone thickness?"

When the core fuel is new there is a surplus of fission neutrons and about half of the fission neutrons diffuse out of the core zone and into the blanket. When the core fuel is old the core zone is thicker and most of the fission neutrons remain in the core zone.

An important technical issue that must be addressed to answer the aforementioned core zone thickness question is: "What is the ratio of neutron random walk path length to core zone thickness?" This path length will vary as the core fuel rods age causing the average Pu-239 concentration in the core zone to change.

Neutrons diffuse through the core zone by scattering. At each scatter a neutron loses a small fraction of its kinetic energy. Between successive scatters the number of neutrons reduces due to neutron absorption. Our first concern is that at about (1 / 3) of the neutrons that are released in the core zone must be absorbed by Pu in the core zone to maintain the chain reaction. Hence to sustain reactor criticality the neutron random walk path length in the core zone must be long enough to cause 33% absorption by fissile Pu atoms.

When the core fuel is new about (1 / 6) of the fission neutrons are absorbed by U-238 in the core zone. As the core fuel ages this fraction gradually rises to about (1 / 2).

Neutrons that are not absorbed in the core should be almost totally absorbed in the blanket zones.

The required blanket thickness is relatively independent of reactor power.

The average concentrations of Pu-239 and U-238 atoms in the core is a function of the core fuel design. These concentrations determine the rate of absorption of neutrons along a neutron random walk path.

This web page last updated March 26, 2021.