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XYLENE POWER LTD.

FNR HEAT TRANSPORT SYSTEM

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

INTRODUCTION:
A nuclear reactor produces heat. That heat is used to produce high pressure steam. Then expansion of that steam through a turbine drives a line synchronous generator to produce 60 Hz 3 Phase electric power.

This web page describes how heat is transported from the FNR primary liquid sodium pool to the steam generators in the turbogenerator halls.

This web page also addresses some technical issues that are common to multiple heat transfer loops.

In a FNR the primary sodium pool contains pure sodium due in part to its superior neutronic proreties. In a FNR the secondary heat transport loop is filled with NaK because the NaK remains a liquid over the temperature range from 15 degrees C to 460 degrees C.

In the scientific literature NaK is a eutectic consisting of about 77% K, 23% Na which has a melting point of -12 degrees C. However, a problem with using this eutectic is that sooner or later there will be an intermediate heat exchange bundle leak that leads to K polluting the sodium pool. Purifying the sodium pool is a multimillion dollar expense. Hence, it is desirable to minimize this problem. Since the whole purpose of using NaK is to bring the melting point of sodium down to room temperature, there is no need to use such a large fraction of K. The literature indicates that 60% Na,40% K has a melting point of 20 degrees C, which may be sufficient for our purposes. Hence, on this website, unless otherwise noted, the term NaK refers to an alloy containing 60% Na and 40% K.

In a liquid sodium cooled Fast Neutron Reactor (FNR) power plant, due to the chemical incompatibility between sodium and water, for safety purposes the primary sodium is triple isolated from the steam generator water. Heat moves from the atmospheric pressure (0.1 MPa) primary sodium to higher pressure (0.5 MPa) secondary NaK by thermal conduction through the intermediate heat exchange bundles that are immersed in the primary sodium pool. The secondary liquid NaK then conveys the heat to NaK-salt heat exchangers which are installed in heat exchange galleries located outside the upper perimeter of the FNR's primary sodium pool enclosure.

Then the heat moves from the secondary NaK through the NaK-salt heat exchangers to atmospheric pressure (0.1 MPa) molten nitrate salt by thermal conduction. The molten nitrate salt conveys the heat through below grade pipes to steam generators that are located in turbogenerator halls on the opposite side of the laneway around the nuclear building.

The steam generators produce high pressure steam which is fed to a tuurbogenerator which expands the steam to produce electricity.

The resulting low pressure steam is condensed. The latent heat of vaporization is harnessed for district heating.


 

The system design approach is to optimize the performance of a 21 MWt (7 MWe) heat transport circuit. Then for a particular FNR up to 48 identical independent heat transport circuits are used to supply heat for up to 8 turbogenerators that collectively output 300 MWe of electricity plus 700 MWt of low grade heat.

FNR Site Plan

The 700 MWt of low grade heat is delivered to four district heating pipe loops. Each district heating loop has 4 X 24 inch diameter buried pipes entering the FNR Power Plant site and 4 X 24 inch diameter pipes leaving the FNR Power Plant Site. Heat that is not used in district heating system is dissipated via 16 geographically distributed small cooling towers, four of which are located at the corners of the FNR Power Plant site.

The use of multiple identical heat transfer circuits and electricity generators enables efficient equipment maintenance while continuing uninterrupted electricity and heat supply services.

This web page provides an overview of the FNR heat transport system. Other web pages focus on the design details of the major heat transport circuit components including the Intermediate Heat Exchange Bundle, FNR NaK Loop, Induction Pump, NaK-Salt Heat Exchanger, FNR Nitrate Salt Loop and Steam Generator.
 

HEAT TRANSPORT OVERVIEW:
In a liquid sodium cooled Fast Neutron Reactor (FNR) for safety purposes the systems that transport heat out of the primary sodium pool use both an isolated NaK circuit and an isolated nitrate salt/oil circuit between each immersed intermediate heat exchange bundle and the corresponding steam generator. There is an induction type NaK circulation pump with a three way diverting valve in the NaK return pipe from the NaK-salt heat exchanger to the intermediate heat exchange bundle. There is a magnetically coupled pump in the nitrate salt/oil return pipe from the remote nitrate salt and oil dump tanks to the NaK-salt heat exchanger. The nitrate salt dump tanks have electric heaters to remelt the nitrate salt when necessary. One of the nitrate salt tanks can be used to raise the temperature of circulating nitrate salt.

The liquid level in the NaK dump tanks is controlled via the argon pressure over the NaK dump tanks. This gauge air pressure varies from zero when the dump tanks are full to 0.5 MPa when the NaK dump tanks are almost empty.

The liquid level in the nitrate salt dump tanks is controlled via the air pressure over the nitrate salt dump tanks. This gauge air pressure varies from zero when the dump tanks are full to 0.1 MPa when the nitrate salt dump tanks are almost empty.

The nitrate salt circuit is vented to tha atmosphere via ball checks at both ends to ensure that the nitrate salt pressure is always lower than the water/steam pressure in the steam generator and is always lower than the NaK pressure. The NaK pressure is maintained by the argon pressure over the NaK loop.

In the event that the NaK level or NaK argon pressure decreases the air pressure over the salt dump tanks is released which causes the molten salt to drain out of the NaK-salt heat exchanger and the extended nitrate salt pipes and flow into the nitrate salt dump tanks. There are corresponding heat transfer oil dump tanks. This arrangement prevents either nitrate salt or heat transfer oil entering the NaK loop via a NaK-salt heat exchanger tube rupture.

HEAT TRANSPORT LOOP ISOLATION:
There are 48 identical independent heat transport circuits, 6 associated with each of the 8 heat exchange galleries located around the perimeter of the primary sodium pool. Failure of any individual heat transport circuit does not cause a failure of the whole. Likewise, any electricity generator can be operated at part power using only a fraction of its 6 allocated heat transport circuits.

Each intermediate heat exchange bundle supplies hot NaK to a dedicated NaK-salt heat exchanger. Each NaK loop has three parallel connected dedicated NaK dump tanks, a dedicated electric induction pump, a dedicated argon filled cushion tank and dedicated pressure relief vents. Any heat transport circuit can be shut down for service while the other heat transport circuits remain in operation.

Each of eight heat exchange galleries has six associated NaK heat transport circuits. Each heat transport circuit has a full load capacity to transport:
1000 MWt / (6 X 8) heat transport circuits = 20.833 MWt / heat transport circuit..

Each heat transport circuit transfers up to 20.833 MWt of heat which in turn can be used by the turbogenerator to provide:
20.833 MWt X 0.300 = 6.25 MWe
of electricity. Thus the maximum possible FNR electricity output is limited by the heat transport circuits to about:
48 X 6.25 MWe = 300 MWe

Each NaK heat transport loop uses 12 inch inside diameter (ID) schedule 40S stainless steel pipe. This pipe has an OD of 12.75 inch, a wall thickness of 0.375 inch and a linear weight of 49.56 lb / ft.

Each nitrate salt loop uses 8 inch schedule 40S stainless steel pipe, 8.625 inch OD wih a wall thickness of 0.322 inch and the pipe mass per unit length is 42.5 kg / m.

At full load the NaK differential temperature drop across each the intermediate heat exchange bundle is about 110 degrees C, and the differential temperature drop across the nitrate salt pipe loop is about 50 degrees C. The maximum liquid flow velocity in the pipes is chosen to be about 3 m / s. At part load the differential temperature across the intermediate heat exchanger remains almost constant but the NaK differential temperature across the NaK-salt heat exchanger falls due to the action of the three way valve.

The thermal conductivities of the Na and NaK are relatively high, so the NaK temperature closely follows the primary Na temperature, limited only by the thermal conductivity of the intermediate heat exchange bundle tubes.

The thermal conductivity of the molten nitrate salt is lower than the thermal conductivity of NaK and in the NaK-salt heat exchanger the nitrate salt flow is laminar, so there is a significant temperature drop between the NaK loop and the nitrate salt loop. This temperature difference also causes significant compressive stress in the NaK-salt heat exchange tubes leading to tensile stress in the NaK-salt heat exchanger shell.

The nitrate salt flow through the steam generator tubes is turbulent, which enhances heat transfer. The thermal stresses in the steam generator are complex. The low end nitrate salt temperature is pinned at 320 C to 330 C by the water temperature at the bottom of the steam generator which is a function of the steam pressure setpoint. Along the steam generator tubes the tube temperature above the steam generator water level is set by the contained molten nitrate salt temperature whereas below the water level the steam generator tube temperature is close to the water temperature.
 

NITRATE SALT LOOP TEMPERATURE MAINTENANCE:
During normal reactor operation the nitrate salt temperature must be maintained above 320 degrees C to prevent NaOH depositing on the inside surface of the NaK-salt heat exchanger tubes. Hence during normal reactor operation the NaK temperature is always kept above 330 degrees C. This temperature prevents deposion of NaOH and some other metal hydroxides on cool heat exchange surfaces.

Below a nitrate salt temperature of about 280 degrees C the nitrate salt can potentially freeze and might no longer transport heat. In order to cool the primary sodium pool down to 120 degrees C, as is required for reactor fuel changes and for intermediate heat exchange bundle service, oil cooling in place of molten nitrate salt cooling is required. To enable cooling of the primary sodium pool down to 120 degrees C the nitrate salt is drained to its dump tank and is replaced by an oil type heat transfer fluid. The steam bypass valve from the steam generator to the turbogenerator condenser is openned. Water in the steam generator evaporates and cools the oil and hence the NaK down to about 110 degrees C which cools the primary sodium pool down to about 120 degrees C.
 

HEAT EXCHANGE TUBE LENGTH, OD and ID:
Each FNR Heat Transport Circuit involves three shell and tube type counter flow heat exchangers: the intermediate heat exchanger, the NaK-salt heat exchanger and the steam generator. These heat exchangers involve 5 m to 6 m long heat exchange tubes which are only supported at their ends. From a heat transport perspective, the smaller the tube diameter the better, because a smaller diameter tube allows a larger heat transfer surface area. However, there are practical limitations on the unsupported tube length and the tube OD and ID due to the torque on the tube ends exerted by the weight of the tube when the long axis of the heat exchange bundle is horizontal, such as during truck transport. It is shown herein that, due to lack of support along the tube length, it is impractical to make these tubes too small in diameter. This issue constrains the ultimate heat exchange surface area.

Define:
Rho = density of tube material
Ri = Tube inside radius
Ro = Tube outside radius
Pi = 3.14159265
X = distance along tube measured from the supporting end
L = tube length
g = gravitational acceleration
Sy = tube material yield stress
Z = height from tube center line
S= tube material stress at height Z fromthe tube center line.

The applied torque Ta exerted by the tube weight on its end is:
Ta = Integral from X = 0 to X = (L / 2) of:
Pi (Ro^2 - Ri^2) dX Rho g X
= Pi (Ro^2 - Ri^2) Rho g (1 / 2) (L / 2)^2
= Pi (Ro^2 - Ri^2) Rho g L^2 / 8

A circle is described by the formula:
Y^2 + Z^2 = R^2
or
Y^2 = R^2 - Z^2
or
Y = [R^2 - Z^2]^0.5

At any particular value of Z the value of Y on the inside surface of the tube is:
Yi = [Ri^2 - Z^2]^0.5
and the value of Y on the outside surface of the tube is:
Yo = [Ro^2 - Z^2]^0.5

Hence for Z < Ri:
Yo - Yi = {[Ro^2 - Z^2]^0.5 - [Ri^2 - Z^2]^0.5}

For Z > Ri, Yi = 0 which gives:
Yo = {[Ro^2 - Z^2]^0.5}

Assume that the tube material stress S(Z) varies linearly from S = 0 at Z = 0 to S = So at Z = Ro.

Hence the opposing torque To is given by:
To = Integral from Z = 0 to Z = Ri of:
4 (Yo - Yi) dZ So (Z / Ro) Z
+ Integral from Z = Ri to Z = Ro of:
4 Yo dZ So (Z / Ro) Z

Hence the opposing torque To is given by:
To = Integral from Z = 0 to Z = Ri of:
4 {[Ro^2 - Z^2]^0.5 - [Ri^2 - Z^2]^0.5} dZ So (Z / Ro) Z
+ Integral from Z = Ri to Z = Ro of:
4 {[Ro^2 - Z^2]^0.5} dZ So (Z / Ro) Z
 
= Integral from Z = 0 to Z = Ri of:
4 Ro^3 {[1 - (Z / Ro)^2]^0.5 - [(Ri / Ro)^2 - (Z / Ro)^2]^0.5} d(Z / Ro) So (Z / Ro) (Z / Ro)
+ Integral from Z = Ri to Z = Ro of:
4 Ro^3 {[1 - (Z / Ro)^2]^0.5} d(Z / Ro) So (Z / Ro) (Z / Ro)

Define:
V = Z / Ro
Then:
To = Integral from V = 0 to V = (Ri / Ro) of:
4 Ro^3 {[1 - V^2]^0.5 - [(Ri / Ro)^2 - V^2]^0.5} V^2 dV So
+ Integral from V = Ri / Ro to V = 1 of:
4 Ro^3 {[1 - V^2]^0.5} V^2 dV So

The maximum acceptable value of So is:
So = Sy / 3

The applied torque Ta must be less than the maximum opposing torque To. Ta < To
gives:
Pi Ro^2 (1 - (Ri / Ro)^2) Rho g L^2 / 8
< Integral from V = 0 to V = (Ri / Ro) of:
4 Ro^3 {[1 - V^2]^0.5 - [(Ri / Ro)^2 - V^2]^0.5} V^2 dV (Sy / 3)
+ Integral from V = (Ri / Ro) to V = 1 of:
4 Ro^3 {[1 - V^2]^0.5} V^2 dV (Sy / 3)

or
Pi (1 - (Ri / Ro)^2) Rho g (L^2 / 8 Ro)(3 / 4 Sy)
< Integral from V = 0 to V = (Ri / Ro) of:
{[1 - V^2]^0.5 - [(Ri / Ro)^2 - V^2]^0.5} V^2 dV
+ Integral from V = (Ri / Ro) to V = 1 of:
{[1 - V^2]^0.5} V^2 dV

or
Pi (1 - (Ri / Ro)^2) Rho g (L^2 / 8 Ro)(3 / 4 Sy)
< Integral from V = 0 to V = 1 of:
{[1 - V^2]^0.5 V^2 dV
- Integral from V = 0 to V = (Ri / Ro) of:
[(Ri / Ro)^2 - V^2]^0.5} V^2 dV

Hence the heat exchange tube outside radius Ro must be sufficiently large to ensure satisfaction of this inequality.

Try substitution:
V = sin U
{(1 - V^2)^0.5} = cos U
dV = cos U dU
giving:
Integral from V = 0 to V = 1 of:
{[1 - V^2]^0.5} V^2 dV
= Integral from U = arc sin(0) to U = arc sin 1 of:
cos^2 U sin^2 dU = (1 / 8)[U - (sin 4 U) /4]|U = arc sin 1
- (1 / 8) [U - (sin 4 U) / 4]|U = arc sin 0
= (1 / 8)[U - (sin 4 U) /4]|U = (Pi / 2)
- (1 / 8) [U - (sin 4U) / 4]|U = 0
= (1 / 8)[(Pi / 2)]

 

Now consider:
Integral from V = 0 to V = (Ri / Ro) of:
[(Ri / Ro)^2 - V^2]^0.5} V^2 dV

= Integral from V = 0 to V = (Ri / Ro) of:
(Ri / Ro)[1 - (Ro / Ri)^2 V^2]^0.5 V^2 dV

Try substitution:
(Ro / Ri) V = sin U
V^2 = (Ri / Ro)^2 sin^2 U
[1 - (Ro / Ri)^2 V^2]^0.5 = cos U
dV = (Ri / Ro) cos U dU

Then:
Integral from V = 0 to V = (Ri / Ro) of:
(Ri / Ro)[1 - (Ro / Ri)^2 V^2]^0.5 V^2 dV

= Integral from U = arc sin 0 to U = arc sin 1 of:
(Ri / Ro) cos U (Ri / Ro)^2 sin^2 U (Ri / Ro) cos U dU
= Integral from U = 0 to U = (Pi / 2) of:
(Ri / Ro)^4 cos^2 U sin^2 U dU
= (Ri / Ro)^4 (1 / 8)[U - (sin 4 U) /4]|U = (Pi / 2)
- (Ri / Ro)^4 (1 / 8)[U - (sin 4 U) /4]|U = 0
= (Ri / Ro)^4 (1 / 8)(Pi / 2)

Thus the inequality:
Pi (1 - (Ri / Ro)^2) Rho g (L^2 / 8 Ro)(3 / 4 Sy)
< Integral from V = 0 to V = 1 of:
{[1 - V^2]^0.5 V^2 dV
- Integral from V = 0 to V = (Ri / Ro) of:
[(Ri / Ro)^2 - V^2]^0.5} V^2 dV

 
becomes:
Pi (1 - (Ri / Ro)^2) Rho g (L^2 / 8 Ro)(3 / 4 Sy)
< (1 / 8)[(Pi / 2)] - (Ri / Ro)^4 (1 / 8)(Pi / 2)
or
(1 - (Ri / Ro)^2) Rho g (L^2 / Ro)(3 / 4 Sy)
< [(1 / 2)]{1 - (Ri / Ro)^4}

or
Ro > {(1 - (Ri / Ro)^2) Rho g (L^2)(3 / 2 Sy)} /{1 - (Ri / Ro)^4}

This equation sets the minimum value of Ro for all of the heat exchange tubes in the FNR heat transport system.

Units check: (kg / m^3) (m / s^2) m^2 / (kg m / s^2 m^2) = m

Numerical evaluation:
Rho = 8030 kg / m^3 g = 9.8 m / s
L = 5 m
Sy = 117 X 10^6 Pa

3 Rho g L^2 / 2 Sy
= (3 X 8.03 X 10^3 X 9.8 X 25)m / (2 X 117 X 10^6) = 25.22 X 10^-3 m

Consider tubing which is (1 / 2) inch ID, (5 / 8) inch OD: Then: Ri / Ro = 0.8 (Ri / Ro)^2 = 0.64 (Ri / Ro)^4 = .4096 [1 - (Ri / Ro)^2] / [1 - (Ri / Ro)^4]
= [1 - 0.64] / [1 - 0.4096] = 0.36 / 0.5904 = 0.6097

Hence the corresponding minimum value of Ro is:
0.6097 X 25.22 mm = 15.37 mm.
Hence the contemplated:
(5 / 8) inch OD = 15.875 mm OD
is sufficient with 5 m long heat exchange tubes but is not adequate with 6 m long heat exchange tubes because as L^2 changes from 25 m^2 to 36 m^2 the effect of the L^2 term becomes over whelming. Hence with (1 / 2) inch ID, (5 / 8) inch OD the unsupported heat exchange tube length is limited to 5 m. It is necessary to substantially increase the tube diameter to overcome this issue. This constraint on tube geometry affects many aspects of the FNR heat transport system design.

In summary, for the steam generator the proposed exposed tubes are 0.500 inch ID, 0.625 inch OD, length = 5.00 m. The resulting tube wall thickness is:
(0.625 inch - 0.500 inch) / 2 = 0.0625 inch

An advantage of the smaller tube diameter is that it better withstands the external steam pressure.

In the intermediate heat exchanger and in the NaK-salt heat exchanger it is necessary to increase the tube ID in order to provide the required cross sectional area for NaK flow. Increasing the tube ID to (3 / 4) inch greatly improves the NaK flow. The minimum required number of tubes to match the cross sectional area of the NaK piping becomes:
[12 inch / (3 / 4) inch]^2 = 256

Assume that the tube OD is 7 / 8 inch. Then:
Ri / Ro = 6 / 7
(Ri / Ro)^2 = 0.7346
(Ri / Ro)^4 = 0.53977
[1 - (Ri / Ro)^2] / [1 - (Ri / Ro)^4]
= [1 - 0.7346] / [1 - 0.53977]
= 0.2654 / 0.46023
= 0.576668

For L = 6 m:
3 Rho g L^2 / 2 Sy
= (3 X 8.03 X 10^3 X 9.8 X 36)m / (2 X 117 X 10^6) = 36.32 X 10^-3 m

Hence Ro must be greater than:
0.576668 X 36.32 mm = 20.944 mm

(7 / 8) inch X 25.4 mm / inch = 22.225 mm,<
which satisfies the inequality. Hence the intermediate heat exchange tubes can be 6 m long if they are (3 /4) inch ID. (7 / 8) inch OD.

In summary, without consideration of thermal stress, the tubes in the intermediate heat exchange bundle and in the sodium-salt heat exchanger are (7 / 8) inch OD, (3 / 4) inch ID and 6 m long. The tubes in the steam generator are (5 / 8) inch OD, (1 / 2) inch ID and are 5 m long.
 

THERMAL STRESS:
Thermal stress calculations are very important but are beyond the present scope of this document. For example, in the NaK-salt heat exchanger the tube temperature will be consistently higher than the shell temperature leading to linear compressive stress in the tubes and linear tensile stress in the shell. It may be necessary to allow the tube sheets to flex to compensate for this issue. It may be necessary to have an untubed perimeter region around the tubed region to permit this flexing. This matter is governed by ASME Fired Pressure Vessel code.

Note that this matter is more complex than it appears on the surface. In a conventional fire tube boiler the tube walls largely operate at the temperature of the surrounding water, not at the contained hot gas temperature. Since the water temperature also sets the shell temperature this issue provides a high degree of stress relief that will not occur in a liquid to liquid heat exchanger. In a liquid to liquid heat eachanger another thermal stress relief method, such as coiled tubes, may be required.
 

FLUID PRESSURE CONTAINMENT:
Irrespective of thermal stress, the fluid pressure must always be safely contained. In this respect there are two formulae that are frequently used on this web site.

The first is Barlow's formula for calculating hoop stress in a cylinder containing a pressurized fluid. In Barlow's formula the applied force F is:
F = P D L
where:
P = pressure difference acrosss the cylinder wall;
D = inside diameter;
L = a unit length of the cylinder.

In Barlow's formula the resisting force is:
F = S (2 W) L
Where:
S = hoop stress
W = wall thickness

At force equilibrium:
P D L = S (2 W) L
or
P = S (2 W) / D

In any matter potentiallyinvolving personnel life safety the maximum acceptable value of S is Sy / 3, where:
Sy = cylinder material yield stress

Thus the maximum safe fluid pressure Pm in a cylinder is:
Pm = [2 Sy W] / [3 D]
 

The second important formula is to calculate the relationship between the pressure across a uniform disc that is supported at its perimeter and the maximum internal stress in the disk material.

Define:
T = disc thickness
D = disc diameter
R = a radius from the disc center
P = pressure across the disc
Z = axial distance measured from the center of the disc.

The applied torque transferred to the edge of the disc by the pressure is given by:
Integral from R = 0 to R = (D / 2) of:
P 2 Pi R dR [(D / 2) - R)
= P 2 Pi (D / 2)(1 / 2) (D / 2)^2 - P 2 Pi (1 / 3) (D / 2)^3
= P 2 Pi (1 / 6) (D / 2)^3

Assume that the resisting torque is zero half way through the thickness of the disk and increases to reach a maximum at the disc surfaces. Let Sm = maximum stress at surface of disc.
Then S = Z Sm / (T / 2)
= 2 Z Sm / T

Then the resisting torque is:
Integral from Z = 0 to Z = (T / 2) of:
2 {S 2 Pi D dZ Z}
= Integral from Z = 0 to Z = (T / 2) of:
2 {(2 Z Sm / T) 2 Pi D dZ Z}
= [8 Sm Pi D / T] [Z^3 / 3]|Z = (T / 2) = [8 Sm Pi D / 3 T] [T / 2]^3
= [Sm Pi D / 3] [T]^2

At equilibrium the applied torque equals the resisting torque, or:
P 2 Pi (1 / 6) (D / 2)^3 = [Sm Pi D / 3] [T]^2
or P (D^2 / 8) = [Sm] [T]^2

In general, for life safety the maximum value of Sm is Sy / 3. Thus the maximum value of pressure P is:
P = 8 (Sy / 3) (T / D)^2
or rearranging:
T^2 = 3 D^2 P / 8 Sy
or T = D [3 P / 8 Sy]^0.5
 

EXAMPLE:
Consider a steam generator with an outside diameter of 48 inches. Barlow's formula gives:
Pm = [2 Sy W] / [3 D]
or
[3 Pm / 2 Sy] = [W / D]

However for this example:
D + 2 W = 48 inch
or
D = 48 inch - 2 W
or W / D = W / (48 inch - 2 W)
giving:
[3 Pm / 2 Sy] = W / (48 inch - 2 W)
or
(48 inch - 2 W)[3 Pm / 2 Sy] = W
or
W [1 + 2 (3 Pm / 2 Sy)] = 48 inch (3 Pm / 2 Sy)
or
W = 48 inch (3 Pm / 2 Sy) / [1 + 2 (3 Pm / 2 Sy)]

In the case of the steam generator where:
Pm = 12 MPa
Sy = 117 MPa
[3 Pm / 2 Sy] = [W / D] = 48 inch / 234 MPa giving: W = 48 inch (3 Pm / 2 Sy) / [1 + 2 (3 Pm / 2 Sy)]
= 48 inch (36 MPa / 234 MPa) / [1 + 72 MPa / 234 MPa] = 48 inch (36 /234) / [306 / 234] = 48 inch [36 / 306) = 5.647 inch

Hence:
D = 48 inch - 2 W
= 48 inch - 11.29 inch
= 36.7 inch

We can now calculate the minimum required solid end cap thickness T using: Recall that for the end cap:
T = D [3 P / 8 Sy]^0.5

= 36.7 inch [36 MPa / 8 (117 MPa)]^0.5
= 36.7 inch [0.196116]

= 7.197 inch

This end cap thickness must be increased to account for loss of material near the perimeter due to tube holes. Assume that the tubes are (5 / 8) inch OD and spaced 1.00 inch center to center. The effective tube sheet perimeter length is reduced to (3 / 8) of its original value. however, the tube sheet becomes thicker. The resisting torque is proportional to the perimeter length and to T^2. To maintain the same overall strength, as the perimeter length drops by fraction (3 / 8) the Thickness T must increase by:
(8 / 3)^0.5 = 1.633

Thus with (5 / 8) inch diameter tube holes on 1.00 inch staggered centers the required end cap thickness becomes:
7.197 inch X 1.633 = 11.753 inch

Note that the required side wall thickness and end cap thickness greatly reduces the surface area available for heat exchange.
 

MOLTEN SALT HEAT TRANSPORT:
The molten salt acts as a thermal fluid and transports heat from each NaK-salt heat exchanger under the adjacent laneway, to a turbine hall which contains the corresponding steam generator. The salt return pipe comes back under the laneway to the NaK-salt heat exchanger. These two nitrate salt pipes must monotonically slope to nitrate salt dump tanks which are located at the pipe low points. The nitrate salt dump tanks must be at a lower elevation than both the sodium-salt heat exchanger and the steam generator to enable gravity drainage of nitrate salt from the sodium-salt heat exchanger and from the steam generator to the nitrate salt dump tanks.

The two end high points in each nitrate salt circuit are vented to the atmosphere via 16 inch diameter vents with top ball checks which are sufficiently tall to allow for the change in nitratre salt level due to the nitrate salt pump pressure differential.

Thus, when the air pressure over the nitrate salt dump tanks is released, provided that the nitrate salt is above 280 degrees C, all the nitrate salt in the nitrate salt loop drains into the nitrate salt dump tanks.

The nitrate salt circulation pump is magnetically coupled to avoid hot salt leakage at the pump mechanical seal. To give this pump positive suction head the pump is located at a pipe loop low point close to the discharge from the nitrate salt dump tanks. However, this pump requires air pressure over the nitrate salt dump tank to provide the pump its required suction head.

In the event of a NaK-salt heat exchanger tube failure the higher pressure NaK will enter the molten nitrate salt circuit where it will rapidly chemically react with the molten salt producing nitrogen. The nitrogen will displace salt in the NaK-salt heat exchanger shell, and will force molten nitrate salt to discharge out the adjacent nitrate salt vent.

As the NaK loses pressure and its level decreases the air pressure over the nitrate salt dump tank is released so that the remaining salt in the NaK-salt heat exchanger will drain to the nitrate salt dump tank. The nitrogen producing chemical reaction will continue as long as there is any NaK above the NaK-salt heat exchanger tube rupture. Thus the salt vent diameter and the various pressure ratings must be sufficient to safely manage this rapid nitrogen production and discharge.

As soon as the nitrate salt level drops below the bottom of the NaK-salt heat exchanger the NaK should be dumped to the NaK dump tanks.

An important ongoing operating issue is maintenance of sufficient thermal flux and molten salt flow to prevent the molten salt from freezing in the external pipes and in the steam generator.

The steam pressure in the steam generator shell must be set sufficiently high to keep the steam generator water temperature and hence the molten salt return temperature well above the salt melting point (280 degrees C). The molten salt supply upper temperature is limited by the NaK temperature and the NaK flow rate. The molten salt return temperature must kept above 280 degrees C to prevent the salt freezing in the pipe and above 320 degrees C to prevent NaOH in the NaK depositing on heat exchange surfaces.

If the molten salt temperature falls below its melting point there will be no heat transport away from the NaK-salt heat exchanger. When it is necessary to cool the primary sodium below 320 degrees C for service or other purposes, at temperatures below 280 C heat should be removed from the NaK using oil cooling instead of salt cooling. The nitrate salt is drained to its dump tank and the nitrate salt dump tank isolation valves are closed. Then oil from the oil dump tanks is used to fill the nitrate salt circuit. This oil is circulated using the nitrate salt pump. The steam generator valve to the condenser is openned. Evaporation of water in the steam generator will extract heat from the oil and hence the NaK and hence the primary sodium pool. The steam generator water level control system will automatically add additional water as the water in the steam generator evaporates.
 

EQUIPMENT STAGGER:
In the heat exchange galleries and in the turbogenerator hall the equipment relating to each of the independent heat transport systems is laid out in parallel rows with a row center to row center spacing of 1.5 m. However, the flanges for the steam generators and the NaK-salt heat exchangers are 2.4 m in diameter before application of insulation. To prevent flange clashes it is essential that the equipment be staggered along the rows such that these flanges do not clash. To achieve this objective on every second row the units with wide flanges are shifted by at least:
1.2 m (3)^0.5 = 2.078 m ~ 2.1 m
with respect to the unshifted units.

The benefit of this equipment staggering is a considerable reduction in the floor space requirement.

The minimum room inside length required for this equipment layout is:
5 (1.5 m) + 2 (1.25 m) = 7.5 m + 2.5 m = 10.0 m

In the heat exchange galleries the internal width allownace is 8.0 m. In the turbogenerator halls the width allowance for the steam generator related equipment is 8.5 m + allowance for discharge steam piping.
 

BLACKSTART:
Assume that the primary sodium pool temperature is initially above 120 degrees C.

Assume that initially the NaK and the nitrate salt are in their dump tanks.

The first step is to apply argon pressure over the NaK dump tank to fill the NaK loop.

Then turn on the NaK induction pump. The NaK temperature should rise to the primary sodium pool temperature.

Transfer oil into the nitrate salt loop.

Raise the primary sodium temperature by movable fuel bundle insertion up to about 280 degrees C. The oil temperature will rise with the NaK temperature.

Electrically heat the nitrate salt in its dump tank to about 400 degrees C.

When the oil reaches 280 degrees C the drain this hot oil to its dump tanks.

Then apply air pressure over the nitrate salt dump tanks to transfer the nitrate salt into the nitrate salt loop. The nitrate salt tanks require a dedicated molten salt liquid level sensor to regulate their cover air pressure. Turn on the nitrate salt pump.

The nitrate salt temperature should rise to the NaK temperature.

Enable the steam generator water injection pump. The water level in the steam generator should rise to its set point. This water will form steam at a rate determined by the flow rate of NaK through the intermediate heat exchange bundle.

Raise the primary sodium pool temperature to 460 C. The presssure in the steam generator will rise to about 11.25 MPa at which point the steam PRV should open releasing steam to the turbine.

While producing steam at low power set the turbine slightly below 1800 RPM. As the generator output voltage reaches phase synchronization, close the contactor.

Now gradually increase the NaK flow rate through the intermediate heat exchanger to increase the electricity generator output.

During black start only one heat transport circuit is started at a time to minimize the auxiliary power required for electric heating during black start.

Once the turbine is operating electricity can be generated and the system no longer requires auxiliary power for continuation of further black start steps. Thus there must be enough auxilliary power to fully turn on at least one heat transport circuit.
 

STEAM GENERATOR TUBE FAILURE:
A steam generator tube failure will cause injection of steam / water into the molten nitrate salt/oil. The water will immediately form steam which will expand blowing molten salt/oil out the steam generator molten salt vent to the atmosphere. A sudden molten salt pressure or level rise in the steam generator salt vent indicates a steam generator tube failure.
 

MAINTENANCE:
There is no radioactivity in the heat exchange galleries, which allows safe service work or NaK fire suppression in selected heat exchange galleries without causing a total reactor shutdown.
 

DIAGRAM:
A diagram showing an end view of a heat exchange gallery. Each gallery has 6 heat transport loops, one behind the other. Note that the NaK-salt heat exchangers are staggered in position, so that part of the 2nd loop is visible behind the first loop.

The left hand side of this diagram shows the intermediate heat exchange bundle and the NaK pipes. This diagram shows the molten salt heat transport pipes on the right hand side and the three parallel connected NaK dump tanks in the lower left middle. The horizontal induction pump, the NaK flow meter and the vertical NaK-salt heat exchanger are in the middle of the diagram. Above the NaK-salt heat exchanger from left to right are the NaK argon filled cushion tank and the molten nitrate salt/oil pressure relief vent.

Note the dedicated steel I beam equipment supports. The maximum width of each such I beam is 0.20 m to allow installation and subsequent replacement of the 1.3 m wide NaK dump tanks.

Note that NaK-salt heat exchanger staggering enables a NaK-salt heat exchanger shell diameter of 1.2 m (~ 48 inches) and flange diameter of 2.4 m. Note that the NaK-salt heat exchanger centerline to end wall clearance is 1.25 m which is barely sufficient for the NaK-salt heat exchanger end manifold flanges + insulation.

The FNR site plan shows the 2.0 m wide space between adjacent heat exchange galleries that is dedicated to the airlocks that are required for moving fuel bundles and intermediate heat exchange bundles from their truck load/unload points into or out of the primary sodium pool space.
 

HEAT EXCHANGE GALLERY LOWER LEVELS:
Each heat exchange gallery has a lower level where the NaK dump tanks are located. Personnel access to the various heat exchange gallery levels is via a stairwell at the gallery end farthest from the airlock truck load/unload point.

The electric drives for the NaK induction pumps are wall mounted adjacent to the induction pumps.

Equipment in the heat exchange galleries is installed and removed from above using a mobile crane parked at the airlock truck load/unload point. The roof over the heat exchange galleries must be easily removable and replaceable.

There must be a large air vents in heat exchange galleries for outside air cooling.

An important issue in the heat exchange gallery is isolation of potential NaK drips. A likely source of these drips are the NaK pipe flange connections. Drip pans should be provided to collect dripped NaK.

In the basement under each heat exchange gallery is an isolated space that is used for an argon bladder. This space is air flow connected to the service access space under the pool deck. Any water penetrating this space from the outside must flow along the floor and into the FNR bottom drain located about 18 m below grade.
 

INDUCTION PUMP:
Induction pumps are used to circulate the NaK. The induction pumps must be sized to overcome the flow pressure head in the NaK loops. Note that these pumps should be located on the low temperature return pipes near the primary sodium pool deck level to ensure both cool operation and sufficient positive suction head.

The induction pump operates by inducing a circular current in the liquid NaK. This current crosses a radial magnetic field component and hence experiences an axial force. External 3 phase coils, analogous to the stator coils of a 3 phase AC motor, create a suitable time varying magnetic field.

In normal operation the pumped NaK temperature is about 340 degrees C and the induction pumps are oil cooled to protect the electrical insulation from heat damage.

When the nitrate salt cooling of the NaK-salt heat exchanger is replaced by oil cooling the NaK temperature at the induction pump will fall to about 110 C, at which point the induction pump does not need oil cooling.

However, under circumstances when the NaK-salt heat exchanger is uncooled either natural or pumped circulation of the NaK can potentially cause the NaK temperature at the induction pump to rise to about 460 degrees C. Under these circumstances the induction pump can easily be damaged if there is insufficient pumped oil cooling. To prevent wide temperature excursions the NaK induction pump must be stopped while there is a transition from nitrate salt to oil cooling and vice versa.

The induction pumps have 16.000 inch OD schedule 40S (0.375 inch wall) 316 SS input pipes and 12.75 inch OD schedule 40S (0.375 inch wall) 316 SS discharge pipes. The 16.000 inch OD pipe runs through the induction pump but is partially obstructed by the induction pump's internal magnetic flux torpedo.

The ID of the 16 inch pipe is:
16.000 inch - 2 (0.375 inch) = 15.25 inch

Induction pump details are set out at FNR Induction Pump.
 

GASKET CONSTRAINT:
A major constraint on the FNR design is gasket material properties. This FNR operates at too high a (temperature X pressure) product for use of normal elastomeric gaskets. Soft metal or compressed carbon gaskets must be used. Such gaskets do not tolerate pipe misalignment, manifold distortion or high pressures. Hence gasketed mechanical joints need near optical precision fabrication. All the NaK-salt heat exchanger manifolds bottom and top halves as well as the pipe mechanical joints are sealed with such gaskets.The flange bolts must have a smaller TCE than the flange material.
 

PIPE AND POOL THERMAL EXPANSION:
The NaK-salt heat exchangers are in fixed positions with respect to the concrete structure. The intermediate heat exchange bundles move due to connecting pipe thermal expansion and contraction. Also the primary sodium pool inside wall moves due to thermal expansion. When the system is cold the insulation of the cooler intermediate heat exchange bundle supply pipes should be almost touching the primary sodium pool inside wall. When the system is hot there is about a 0.2 m gap between this pipe insulation and the primary sodium pool inside tank wall.
 

FULL LOAD SYSTEM TEMPERATURE PROFILE (deg C):_______
FUEL
CENTER
Primary  
Na HIGH
Primary  
Na LOW
Secondary  
NaK HIGH
Secondary  
NaK LOW
STEAM  
HIGH
STEAM  
LOW
WATER  
HIGH
WATER  
LOW
10%550544322543321503320320____
100%550440340429329440320320____

 

NaK PIPING
At 600 degrees C the yield stress of stainless steel is 117 MPa.

Assume the use of 12.7 inch OD, 12.000 inch ID pipe for the NaK. The flow cross sectional area of each such pipe is:
Pi (6.000 inch)^2 X (.0254 m / inch)^2 = 0.07296 m^2

The pipe yield pressure at 600 deg C is:
117 MPa X (2) (0.350 inch / 12.000 inch) = 6.825 MPa

Hence for safety the NaK pipe working pressure should be less than:
6.825 MPa / 3 = 2.275 MPa
 

Let V = average axial flow velocity of NaK in the 12.7 inch OD pipe. Then:
V = (0.1672 m^3 / s)______ / [0.07296 m^2)]
= 2.010 m / s_______

WELDING:
The manifold welds must be deep penetration equal in quality to the welds used on high pressure natural gas distribution pipelines. Possibly a helium leak detector should be used for confirming weld quality.
 

This web page last updated April 26, 2022

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