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XYLENE POWER LTD.

FNR SECONDARY SODIUM HEAT TRANSPORT SYSTEM

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

INTRODUCTION:
A nuclear reactor produces heat. The most practical way to convert that heat into electricity is to use the heat to produce high pressure steam. The steam expands through a steam turbine which drives a line synchronous generator to produce 60 Hz 3 Phase electric power.

In a liquid sodium cooled Fast Neutron Reactor (FNR) due to the chemical incompatibility between sodium and water for safety purposes there are intermediate heat transport loops between the hot radioactive primary sodium and the steam generators.

This web page provides an overview of the secondary sodium heat transport system and related pipe and dimensional matters. Other web pages focus on the design detials of the Intermediate Heat Exchangers, Induction Pumps and Steam Generators.

The nuclear power plant consists of 56 independent identical heat transport systems so that a failure of individual heat transport systems does not cause a failure of the whole. Individual heat transport systems can be shut down and maintained while the balance of plant continues to operate.
 

SECONDARY HEAT TRANSPORT FLUID:
The FNR requires a secondary heat transport fluid that is compatible with the heat exchange tube material (Inconel 600) and will not chemically react with the hot radioactive primary liquid sodium in the event of an intermediate heat exchange tube failure. This heat transport fluid must to be chemically stable over the temperature range 0 C to 600 C.

This same secondary heat transport fluid must react with water in a predictable manner to allow safe system shutdown in the event of a steam generator tube failure.

To meet these specifications for this FNR medium pressure (~ 7 MPa) non-radioactive sodium is used as the secondary heat transport fluid.
 

INTERMEDIATE HEAT EXCHANGERS:
The intermediate heat exchangers isolate the primary radioactive liquid sodium from the secondary non-radioactive liquid sodium. They also serve as a barrier to other radioactive species in the event of a fuel tube leak.

There is a ring of 56 intermediate heat exchangers that are immersed in the primary sodium pool in a concentric 18 m diameter ring. These heat exchangers are located between the pool surface and 7 m below the pool surface.

The weight of the intermediate heat exchangers is supported by a ring shaped table located in the primary sodium pool about 8 m above primary sodium pool bottom and about 9 m radially from the pool center. This table is supported by a ring of steel columns and the table is horizontally stabilized by the adjacent innermost primary sodium pool liner. The top of this table is covered by a layer of small ball berrings which allow the supported intermediate heate exchangers to move back and forth radially to accommodate thermal expansion/contraction of the primary sodium pool and the radial secondary sodium piping. Apart from thermal expansion the radial position of the intermediate heat exchangers is fixed by the radial secondary piping which in turn is fixed to the steam generators and induction pumps, which are in turn are fixed to the heat exchange gallery concrete structure. Thermal expansion, at points where these pipes pass through gas tight walls, is accommodated by use of metal bellows fittings.

The maximum outside diameter of the intermediate heat exchange manifolds is limited to about:
Pi (18 m) / 60 = 0.94 m = 37.0 inch
so that they will fit in the available space on an 18 m diameter circle in the primary sodium pool.

Hence the intermediate heat exchangers are in nearly fixed positions with respect to the concrete enclosure. In the event of a very severe earthquake the primary sodium pool walls can move op to about 0.5 m _____horizontally in any direction with respect to the concrete enclosure before there is a collision between an intermediate heat exchanger and the adjacent primary sodium pool side wall.

A diagram showing one of 56 induction pump-steam generator pairs is shown below.

This diagram also shows the secondary sodium pipes on the left hand side, the steam headers in the upper right and the secondary sodium drain down tank on the lower right. Note the dedicated columns which support the induction pump and the steam generator.

Note that in the heat exchange galleries adjacent steam generators and induction pumps are staggered in position to allow service access clearance around each unit.
 

FLUID FLOWS:
The FNR secondary sodium loops take advantage of the relatively low density and large thermal coefficient of expansion of liquid sodium to promote natural circulation of the secondary liquid sodium.

Even with no pumping the position of the steam generator and induction pump above the intermediate heat exchanger causes the secondary liquid sodium to naturally circulate.

There is an induction pump for circulating intermediate sodium from the lower manifold cap of the steam generator to the lower manifold cap of the intermediate heat exchanger. A specially engineered induction pump is necessary because of the about 1.0 inch wall thickness of the pipe forming the intermediate sodium circuit.

While this pump normally operates with 330 degree C secondary sodium thei pump must not be damaged by 500 degree C sodium that it might see at times when the steam generator contains no water.

Hot (490 degree C) primary sodium flows into the intermediate heat exchangers just below the pool surface and cooler (340 degrees C) primary sodium is discharged about 6 m below the primary sodium pool surface. Primary sodium flows down outside the intermediate heat exchanger tubes and secondary sodium flows up through the intermediate heat exchanger tubes.

The intermediate heat exchangers are single pass to realize a counter current operation and to minimize material thermal stresses.

In the steam generator secondary sodium flows downwards through tubes in the upper and lower sections of the steam generator and water/ steam flows upwards on the shell side of the steam generator.

Thus in both the intermediate heat exchanger and the steam generator high pressure liquid sodium is inside the heat exchange tubes. If there is a secondary sodium leak from the intermediate heat exchanger tube manifold that sodium will leak into the primary sodium pool.

Potential problems are secondary sodium leaks from the heat transport piping, steam generator, induction pump or overhead expansion tank. In every case the appropriate solutionis to transfer the contained sodiu into a below grade drain down tank to minimize the sizee of a potential sodium fire.

A diagram showing one of 56 intermediate heat exchanger-steam generator pairs is shown below.

This diagram also shows the secondary sodium pipes on the left hand side, the steam headers in the upper right and the secondary sodium drain down tank on the lower right. Note the dedicated columns which support the induction pump and the steam generator.

Note that in the heat exchange galleries adjacent steam generators and induction pumps are staggered in position to allow service access clearance around each unit.
 
 

PROVISIONS FOR SYSTEM MAINTENANCE:
To enable heat transport system service the secondary sodium is transferred into a drain down tank.

Application of argon pressure over the drain down tank and relief of argon pressure from the top of the secondary sodium loop transfers secondary liquid sodium from the drain down tank into the secondary loop. Reversing this procedure allows secondary sodium to gravity flow back into the drain down tank. Secondary sodium is locked into the heat transport loop via use of as freeze plug. When this plug is closed the loop empty volume available to accommodate thermal expansion is drastically reduced.

A liquid sodium detector should be provided at the top of the system to indicate when to close the top argon vent valve. The supply of argon for presurizing the drain down tank and the argon sink from the system top can both be from the primary sodium pool enclosure. Similarly when drain down is required the argon in the drain down tank can be vented to the pool enclosure and after the argon pressure has sufficiently dropped the argon top vent valve can be openned. Note that for safty this argon top vent valve must be vented over the primary liquid sodium pool. Failure or premature openning of this vent valve could cause a high pressure high temperature stream of liquid sodium to be expelled.

If there is a leak in an intermediate heat exchanger the contained sodium will natually flow back into the primary sodium pool when the intermediate heat exchanger is crane lifted.

To expel secondary sodium from the intermediate heat exchanger tubes the secondary sodium level is first drained down to the level of the bottom of the steam generator. Then the secondary sodium in the pipe immediately below the bottom of the steam generator is frozen to form a sodium plug. Then argon pressure is applied to the expansion tank which will drive most of the contained sodium from the intermediate heat exchanger into the drain down tank.

In reality, even after this procedure is complete a small pond of secondary sodium will remain in the bottom manifod of the intermediate heat exchanger. This small pond presents a potential risk to maintenance personnel and a potential fire risk if at some later time oxygen is admitted into the secondary sodium piping. One way to minimize this risk is to have a small tube that connects onto the intermediate heat exchanger lower manifold and to remove this remanent secondary sodium by vacuum suction. In general for safety the flange connections of the intermediate heat exchanger and the radial piping should be closed with blanking plates while the intermediate heat exchanger is still in the reactor argon atmosphere.
 

LOOP REPAIR:
At the low points in the heat transport pipe loops are sealed sodium drain down tanks with sufficient volume to accommodate all the liquid sodium in that secondary heat transport circuit. These drain down tanks have electric immersion heaters for secondary liquid sodium melting/temperature maintenance. Note that these drain down tanks must be rated as pressure vessels and must be fitted with high pressure argon relief valves vented to the argon atmosphere over the primary sodium pool.
 

PROCEDURE FOR INTERMEDIATE HEAT EXCHANGER REPLACEMENT:
Replacing an intermediate heat exchanger involves the following steps:
a) Drain the primary sodium from the intermediate heat exchanger to remove the radiation hazard.
b) Cool down the secondary sodium to 120 deg C;
c) Transfer the secondary sodium in the defective heat transport loop to the loop drain down tank;
d) Sisconnect both secondary sodium service pipes at the flanged connections;
e) Immediately blank off the disconnected pipes;
f) Use a crane to lift out the defective heat exchanger;
g) Transfer the defective heat exchanger to a service vehicle;
h) Lift a replacement intermediate heat exchanger into place using the same crane;
i) Rotate the new heat exchanger so that its connection flanges align with the secondary sodium service pipes; k) Connect the service pipes. During this work try to keep them full of argon. Withdraw blanking plates at the last moment;
l) Make pipe connections with appropriate metal gaskets. Use a laser alignment tool;
m) Test that the system holds argon pressure.
n) Insulate the piping;
o) Transfer secondary liquid sodium from the drain down tank back into the secondary heat transport loop;
 

PROTECTION OF THE INTERMEDIATE HEAT EXCHANGER FROM HIGH TRANSIENT PRESSURES:
In the event of a tube rupture in the steam generator below the steam generator water level there is potential for a violent chemical reaction between the secondary sodium and water used as the turbine working fluid. If this chemical reaction took place in the secondary sodium loop a hydrogen pressure pulse from this reaction might cause a liquid sodium hammer analogous to water hammer, possibly rupturing the intermediate heat exchanger and leading to major facility damage. Hence the secondary heat transport system, including the intermediate heat exchangers, must be designed to safely withstand large transient pressures and the secondary liquid sodium should normally operate at a pressure a bit below the steam pressure. Then a modest secondary sodium pressure rise will reliably indicate the existence of a steam generator tube leak and will stop further fluid flow through that leak. In order for this mechanism to reliably operate the secondary sodium expansion tank must be relatively small and there must be a freeze plug between the secondary sodium circuit and its draindown tank. There must also be a rupture disk bridging the freeze plug to provide instantaneous pressur relief in the event of a steam generator tube leak.

In spite of these measures the intermediate heat exchanger tube side must still have a working pressure rating equal to the steam pressure rating. The aforementioned rupture disk must be able to discharge liquid sodium from the secondary sodium circuit at a rate equal to the rate of high pressure hydrogen formation in that circuit. That rate is limited by the maximum water flow through the steam generator tube rupture which is a function of the steam generator tube diameter and the differential pressure between the steam generator and the secondary sodium.

In a practical accident scenario the water forms hydrogen which raises the secondary sodium pressure to the pressure in the steam generator before starting to drive sodium back through the tube rupture and into the steam generator. Instead of driving sodium into the steam generator it is preferrable to drive sodium into the drain down tank. Hence the rupture disk rating should be approximately equal to the nominal steam pressure and the normal secondary sodium pressure should be sufficiently below the rupture disk rating to prevent unplanned rupture disk operation.

Each secondary sodium heat transport loop is pressurized by expansion and drain down tanks containing variable pressure argon. The drain down tank also acts as an expansion tank and attenuates any pressure pulses in the secondary liquid sodium.
 

DETECTION OF SECONDARY SODIUM LEAKS THROUGH THE INTERMEDIATE HEAT EXCHANGER OR TO THE ATMOSPHERE:
Any leak in a secondary sodium circuit other than to the steam generator shell side will result in loss of argon pressure in the secondary sodium loop expansion tank. Should such a pressure dropoccur that entire heat transport loop should be shut down and the secondary sodium should be drained to the drain down tank by openning the loop freeze plug.
 

SODIUM FIRES:
Other parties using liquid sodium for heat transport have experienced repeated sodium fires. The problem is that when hot high pressure liquid sodium is inside a pipe the sodium tends to leak out via any mechanical joint that is less than perfect. The secondary liquid sodium operating temperature is too high for use of elastomeric gaskets. Once outside the pipe the sodium spontaneously ignites in air. That situation is unacceptable.

A potential problem is secondary sodium leaks from the heat transport piping, steam generator, induction pump, dump tank or overhead expansion tank.

The solution to this problem is to fit every secondary sodium loop with a drain down tank and to enclose all the secondary sodium pipes outside the reactor space in an argon filled jacket. Hence, if secondary sodium leaks it does not immediately ignite. The volume of the leak is limited to the contents of one secondary sodium loop. Use of a large number of secondary sodium loops minimizes the consequence of a single loop failure.

NO RADIATION HAZARD:
An important feature of this heat trasport system design is that normally there is no radiation in the heat exchange galleries. Thus if there is a sodium fire there it can be immediateloy accessed and extinguished without personnel radiation hazard. Further, it may be practical to reduce the thickness of the heat exchange gallery exterior wall, because it is normally not required to act as a radiation barrier.
 

INTERMEDIATE HEAT EXCHANGER OPERATING CONDITIONS:
The tube side of the intermediate heat exchange bundle contains non-radioactive intermediate sodium typically at a pressure of about 7 MPa. Note that the secondary sodium is on the inside of the intermediate heat exchanger tubes. The low temperature limit on the circulated intermediate sodium at full load is 330 degrees C to prevent NaOH precipitation within steam generator heat exchange tubes. The high temperature limit on the circulated intermediate sodium is 520 degrees C at low loads falling to about 480 degrees C at full load. We are assuming a full load 10 degree C temperature difference between the primary liquid sodium and the intermediate liquid sodium. At full load the dry steam in the steam generator will reach:
(480 deg C - 40 deg C) = 440 deg C.

At full load the intermediate sodium can drop to 480 -330 = 150 deg C without threat of NaOH precipitation. There is feed water temperature mixing in the bottom of the steam generator to minimize thermal stress on the immersed steam generator tubes. The feed water temperature rise from 25 deg C to 320 C is realized by feed water recuperator heat recovery from the steam immediately upstream from the turbine condenser followed by water mixing in the bottom of the steam generator.

SYSTEM TEMPERATURE PROFILE (deg C):
FUEL
CENTER
Primary  
Na HIGH
Primary  
Na LOW
Secondary  
Na HIGH
Secondary  
Na LOW
STEAM  
HIGH
STEAM  
LOW
WATER  
HIGH
WATER  
LOW
10%550544322543321503320320____
100%550490340479329440320320____

 

PROCEDURE FOR INTERMEDIATE HEAT EXCHANGER REPLACEMENT:
Replacing an intermediate heat exchanger involves the following steps:
a) Drain the primary sodium from the intermediate heat exchanger to remove the radiation hazard.
b) Cool down the secondary sodium to 120 deg C;
c) Transfer the secondary sodium in the defective heat transport loop to the loop drain down tank by releasing the argon pressure over the drain-down tank;
d) Cut or disconnect all four service pipes;
e) Immediately blank off the cut or disconnected pipes;
f) Use a crane to lift out the defective heat exchanger;
g) Transfer the defective heat exchanger to a service vehicle;
h) Lift a replacement intermediate heat exchanger into place using the same crane;
i) Rotate the new heat exchanger so that its pipe stubs line up with the pipe passage holes in the reactor enclosure wall;
j) Purge the piping with argon and check pipe alignment using sliding sleeves;
k) Connect the service pipes. During this work try to keep them full of argon. Withdraw blanking plates at the last moment;
l) Weld the pipe connections;
m) Insulate the piping;
n) Transfer secondary liquid sodium from the dump tank back into the secondary heat transport loop;
o) Test that the system holds argon pressure.
p) Start the primary sodium flow siphons
 

STEAM GENERATOR
In the steam generator the water/steam is on the shell side of the tubes. The steam generator tubes contain intermediate sodium at a higher pressure than the water/steam. The shell must be pressure tested to 18 MPa.

In the event of a steam generator tube failure water enters the secondary sodium circuit where it generates hydrogen. The transient pressure increase in the secondary sodium circuit causes secondary sodium to flow into its drain down tank and triggers a vent of steam/water from the steam generator to the atmosphere. This pressure relief arrangement protects the intermediate heat exchanger pressure tubes.

INDUCTION PUMPS

Important sub-system components are the secondary sodium induction pumps. These pumps must dependably operate at about 330 degrees C at a liquid sodium pressure of 11.5 MPa. They must not be damaged by 500 degree C secondary sodium and must be pressure tested at 18 MPa.
 

ADVANTAGES OF THIS EQUIPMENT CONFIGURATION:
1) There is no radio activity in the heat exchange gallery allowing fire suppression and service work around the induction pumps and steam generator without a reactor shutdown.

2) Reactor power can be modulated by modulating the secondary sodium flow rate.

3) The airlock design for primary sodium pool access must accommodate intermediate heat exchangers and related piping.

4) There must be enough secondary sodium natural circulation to dependably remove fission product decay heat so that the system remains safe on loss of electric power.
 

DISADVANTAGES OF THIS EQUIPMENT CONFIGURATION:
1) Need thick concrete walls between the primary sodium pool and the heat exchange galleries.

2) Need high pressure (11.5 MPa) secondary sodium circuits between the intermediate heat exchangers and the steam generators.
 

CONTINUE FROM HERE

THERMAL SIPHON CALCULATIONS:
Define:
V = linear sodium velocity in pipe g = acceleration of gravity
Rho = density of liquid sodium
A = pipe cross sectional area
H =verage height of temperature difference
Cp = heat capacity of sodium ~ 0.3 cal / gm-deg C

Assume that the intermediate heat exchanger is mounted so that its center is 5 m above the surface of the primary sodium pool. Then the top of the intermediate heat exchanger tube bundle is 8 m above the top surface of the primary liquid sodium pool. This height is consistent with the sodium vapor pressure constraint. For H = 5 m:
V^2 = 1.176 m^2 / s^2 or
V = 1.0844 m / s

Thermal power = Rho A V Cp (150 deg C) = 0.927 gm /cm^3 X 10^6 cm^3 / m^3 X A X 1.0844 m / s X 1.23 J / gm deg C X 150 deg C
= 185.466 X 10^6 J A / m^2 - s
= 185.466 MWt A / m^2

Thus neglecting viscosity and assuming ideal heat exchanger and reactor performance the maximum heat transport capacity is:
185.466 MWt / m^2 X 8.705 m^2 = 1614.5 MWt.

However, there will be a reduction in intermediate heat exchanger performance because the primary side of the intermediate heat exchanger operates in the laminar flow region. The effective tube wall thickness is increased by about (1 / 8) inch of sodium. At 700 deg K the liquid sodium has a thermal conductivity of 70.53 W / m-deg K.

Hence the temperature drop delta T across the (1 / 8) inch thick liquid sodium boundary layer is given by:
875 X 10^6 Wt / 56 bundles = [(delta T) (70.53 Wt / m-deg K) X 823 tubes X 6 m X Pi X (0.5 inch) / (1 / 8)] inch
or
(delta T) = [875 X 10^6 Wt / [(56 bundles) X (70.53 Wt / m-deg K) X (823 tubes / bundle) X 6 m X Pi X (0.5 inch) / (1 inch / 8)]
= 3.57 deg K

The web page FNR HEAT EXCHANGE TUBES
indicates that at full rated power the temperature drop across the intermediate heat exchanger tube metal wall is 7.40 deg C. Hence the total temperature drop across the intermediate heat exchange bundles at full power is about:
3.57 deg C + 7.40 deg C = 10.97 deg C.

SECONDARY SODIUM CROSS SECTIONAL AREA
The cross sectional area of the rising secondary sodium is:
823 tubes X [Pi (0.37 inch / 2)^2] / tube
= Pi [28.167 inch^2]
= Pi [5.307inch^2]
= Pi [10.614 inch / 2]^2
which indicates secondary sodium pipe of about 10.6 inch ID.

Use Schedule 160 pipe which is 10.12 inch ID, 12.752 inch OD. This choice is justified by the smaller open area of the tubes in the steam generators.

A key issue is whether there is enough natural circulation of secondary sodium with 100 degree C water in the steam generator to remove fission product decay heat.

DO THIS CALCULATION CONTINUE FIXES FROM HERE

The differential pressure established by the falling sodium column is:
P = [(873.2 -849.4) / 2] kg / m^3 x 6 m x 9.8 m / s^2
= 699.72 kg m / s^2-m^2

Neglecting viscosity:
P = Rho V^2 / 2
or
V = [2 P / Rho]^0.5 = [2 (699.72 kg m / s^2-m^2) / (849.4 kg / m^3)]^0.5 = 1.2836 m / s
= maximum possible falling sodium flow velocity

The corresponding falling sodium volumetric flow rate = 1.2836 m / s X 0.3893 m^2 = 0.4996 m^3 / s

This is about twice the required flow rate. However this flow rate will be retarded by viscosity. This flow rate can be further reduced as required by adding a baffle to the primary side of the intermediate heat exchanger.

It is necessary to maintain the design temperature differential across the reactor in order to develop the required primary sodium natural circulation through the reactor.

Note that each intermediate heat exchange tube bundle contains baffles that cause zig-zag downward flow to enhance heat transfer. The baffle design detail may have to be experimentally optimized. Note that the baffle gives each tube bundle an effective open area on the primary sodium side of about 1 m^2_____.

Each intermediate heat exchanger transfers up to 15.625 MWt of heat which in turn can provide up to 5 MWe of turbo-electricity generation. Thus the total reactor electricity output is limited by the heat transport system to about:
56 X 5 MWe = 280 MWe
 

SECONDARY SODIUM CIRCUIT:
The secondary sodium high temperature is about 480 degrees C at full load and 530 degrees C at low load. The secondary sodium low temperature is about 330 degrees C at full load and 321 degrees C at low load. There is a secondary sodium drain to a pressure rated dump tank at a low point on the return secondary sodium pipe between the steam generator and the intermediate heat exchanger. The drain pipe is connectred so as to fully drain the induction pump.
 

TEMPERATURE CONSTRAINT:
At low steam loads the intermediate sodium flow will decrease and the primary sodium discharge temperature from the FNR will rise about 500 degrees C. As the steam load increases the intermediate sodium flow will increase and the intermediate sodium discharge temperature will decrease to about 490 degrees C.

As the primary liquid sodium flows through the reactor at full power its temperature increases from 340 C to 490 C. In this temperature range in a fast neutron flux the fuel tube material HT-9 undergoes goes material embrittlement.
 

MASS FLOW BALANCE:
To attain the desired temperature distribution the intermediate heat exchanger intermediate sodium mass flow rate must be the same as the intermediate heat exchanger primary sodium mass flow rate.
 

SECONDARY SODIUM HEAT TRANSPORT:
Define:
Fmi = secondary sodium mass flow rate (kg / s);
Cpi = secondary sodium heat capacity
= 1.26 kJ / kg-deg K for sodium
Delta Ti = change in intermediate sodium temperature
= 150 deg K
Then for sodium:
Fmi Cpi (Delta Ti) = 875 MWt
or
Fmi = [875 MWt] / [Cps (Delta Ti)]
= {[875 MWt]
/ [(1.26 kJ / Kg-deg K) (150 deg K)]} X {1 kJ / kWt-s} X {10^3 kWt / MWt}
= [(875) / (1.26 X 150)] X 10^3 kg / s
= 4.63 tonnes / s

The corresponding volumetric intermediate sodium flow is:
(4.63 tonnes / s) / (0.927 tonnes / m^3
= 4.99 m^3 / s

Since there are 56 intermediate heat exchangers, the required intermediate sodium volume flow rate in each exchanger is: (4.99 X m^3 / s) / 56 exchangers
= 0.0892 m^3 / s-exchanger
= 0.0892 m^3 / s-exchanger X 60 s / min
= 5.352 m^3 / min
= 0.0892 m^3 / s-exchanger X 3600 s / h
= 321.05 m^3 / hr-exchanger
 

The 12.75 inch OD pipe has an ID given by:
323.9 mm - 2(33.32 mm) = 257.26 mm.

Its inside cross sectional area is:
Pi (0.25726 m / 2)^2 = 0.0519797769 m^2

Thus at full load the average secondary sodium flow velocity in this pipe is:
(0.0892 m^3 / s) / (0.0519797769 m^2) = 1.716 m / s

The corresponding intermediate sodium flow rate in the intermediate heat exchanger tubes is:
(321.05 m^2 / hr-exhanger) / (823 tubes / exchanger) = 0.3900 m^3 / hr-tube
= (0.3900 m^3 / hr-tube) X (1 hr / 3600 s)
= 1.08333 X 10^-4 m^3 / s-tube

The corresponding intermediate sodium flow rate in the steam generator tubes is:
(321.05 m^3 / hr-exchanger) / (625 tubes / exchanger)
= 0.51368 m^3 / hr-tube
= (0.51368 m^3 / hr-tube) X (1 hr / 3600 s)
= 1.4268 X 10^-4 m^3 / s-tube

The following equations derived on the web page titled FNR PRIMARY SODIUM FLOW can be used to find the pressure drop Pd per round coolant flow tube neglecting natural circulation:
Fv = [Pi Pd Ro^4] / [Muv Zo (N + 2)(N + 4)]BR> where:
Pd = pressure drop along tube in Pa (1 Pa = 1 kg m /s^2 m^2) Fv = volumetric flow rate / tube Pi = 3.14159
Ro = (0.37 inch / 2) X (0.0254 m / inch) = 0.004699 m = tube inside radius
Muv = 3 X 10^-4 N-s / m^2 = sodium viscosity
(N + 2) = Ro [(Rhos Pd) / 2]^0.25 [1 / [Muv Zo]^0.5]
where:
Zo = 6.0 m = tube length
Rhos = 849.4 kg / m^3 = density of sodium at the reactor operating temperature

Recall that:
Fv = [Pi Pd Ro^4] / [Muv Zo (N + 2)(N + 4)]
or
Pd = [Fv / (Pi Ro^4)] [Muv Zo (N + 2)(N + 4)] Equation #1

Recall that:
(N + 2) = Ro [(Rhos Pd) / 2]^0.25 [1 / [Muv Zo]^0.5]
or
N = {Ro [(Rhos Pd) / 2]^0.25 [1 / [Muv Zo]^0.5]} - 2 Equation #2

Try and initial interim value of N = 1.0 in equation #1 and solve for an interim value of Pd.
Substitute that interim value of Pd into equation #2 and solve for a new interim value of N.

Repeat this process itteratively until N and Pd converge.

Then the sum of the Pd values in combination with the exchanger intermediate sodium flow rate give the mechanical load for an ideal circulation pump.

FIX FROM HERE ONWARD

At 600 degrees C the yield stress of pipe steel is 193 MPa.

The yield pressure at 600 deg C is:
193 MPa X (2) (1.594 inch / 12.812 inch) = 48.0 MPa

Hence for safety the secondary heat transport system working pressure should be less than:
48.0 MPa / 3 = 16.0 MPa

The corresponding saturated steam temperature is:
664 deg F = 351 deg C
 

Assume the use of 16.0 inch OD, 12.812 inch ID pipe. The flow cross sectional area of each such pipe is:
Pi (6.406 inch)^2 X (.0254 m / inch)^2 = 0.0831746 m^2

Let V = average axial flow velocity of secondary liquid sodium in the 16 inch OD pipe. Then:
V = (0.1672 m^3 / s) / [0.0831746 m^2)]
= 2.010 m / s

This intermediate liquid sodium flow will develop a momentum change pressure at a sharp 90 degree elbow of:
(2.010 m / s)^2 X 1 m^2 X 927 kg / m^3 = P X 1 m^2
or
P = (2.010 m / s)^2 X 927 kg / m
= 3746 kg / m s^2
= 3746 Pa
= 3746 Pa X 1 bar / 101,000 Pa
= 0.03709 bar

This pressure change is one possible method of measuring the fluid velocity in the pipe.
 

INTERMEDIATE HEAT EXCHANGE BUNDLES:
The intermediate heat exchanger is realized with a single pass vertical tube bundle.

The tube side top connects to the steam generator tube side top via a 12.75 inch OD thick wall pipe. The tube side bottom connects to the steam generator tube side bottom via a 12.75 inch OD thick wall pipe. This pipe contains an induction pump that circulates secondary liquid sodium from the bottom of the steam generator to the bottom of the intermediate heat exchanger. This configuration provides heat exchange counterflow and permits removal and replacement of individual heat exchangers and induction pumps via an overhead crane lift. There is a gravity drain to a secondary sodium dump tank that also acts as a cushion tank. The dump tank is located in the 2 m wide space that is not occupied by a column.
 

INTERMEDIATE HEAT EXCHANGER AND STEAM GENERATOR LOCATION:
Each Steam Generator has a Heat Exchange Gallery length allocation of 1.50 m. These allocations start at the wall common to the air lock. The Heat Exchange gallery width allocations are as follows:
Start at wall common to the primary sodium pool enclosure:
0.50 m space from common wall with primary sodium pool to vertical pipe
0.75 m freeze plug and rupture disk allowance 4.00 m for induction pump and 2 m stagger allowance to steam generator
0.75 m Steam generator maximum radius
2.00 m Width allocation for drain down tank
0.50 m space to inside surface of outside wall
Heat Exchange Gallery inside width = 8.5 m

The next Steam Genertor pair is staggered by 2 m by moving the drain down tank to the opposite side.

At the end of the Heat Exchange Gallery furthest from the airlock is 2.00 m of Heat Exchange Gallery length reserved for a stair well. Thus the overall
Heat Exchange Gallery inside length:
= 7 (1.50 m) + 2.00 m = 12.5 m

SECONDARY SODIUM HEAT EXCHANGE TUBE MANIFOLDS:
The width of the individual heat exchange bundles is limited by the pressure withstand capabilities of the intermediate heat exchanger and steam generator end caps. Assume that the end caps are both bolted and welded.

Standard flanging for nominal 12 inch pipe sets the minimum manifold width at each connection pipe as ______ inches.

Assuming 2 inch thick manifold material and 8 inch wide flanges gives an uninsulated outside width of 24 + 2(10) = 44 inches.

Allowing for 0.2 m (8 inches) of insulation thickness increases the manifold flange width to 1.5 m. Hence the end cap casting must be limited to 1.10 m in diameter. The pressure pipe is 24 inches (0.6096 m) in OD. Thus the maximum casting overlap is given by:
(1.100 m - 0.6096 m) / 2 = 0.2452 m
 

INTERMEDIATE HEAT EXCHANGE TUBE CONFIGURATION:
The intermediate heat exchange tubes are Inconel 600, 20 feet (6.1 M) long. They are 0.500 inch OD, 0.065 inch wall thickness. The heat exchange bundles are single pass and sloped for complete drainage to the dump tank.

Assume that the intermediate heat exchange tubes are located on 0.70 inch rectangular grid to allow external primary liquid sodium to easily penetrate the tube bundle without being so far between the tubes as to cause a heat transfer deterioration.
 

INTERMEDIATE HEAT EXCHANGE BUNDLE SODIUM DRAIN TUBE:
Each intermediate heat exchange bundle has a small diameter drain tube with monotonic slope running from the lowest point inside the lower manifold to a lower point on the primary sodium retrun pipe. This tube ensures complete draindown of primary sodium when argon is admitted into the shell side of the Inttermediate Heat Exchanger.

When it is desired to remove a particular intermediate heat exchanger first pressurized argon is removed from the dump tank head space and is vented to the top of the secondary sodium loop. As a result the entire volume of secondary sodium drains into the drain down tank.

Hence when a heat exchanger is disconnected there will be little hazard due to residual liquid sodium in the pipes and heat exchanger. Note that the pipes must slope monotonically to ensure complete liquid sodium drainage.
 

LOOP ISOLATION:
The heat transport loops are completely isolated from one another. Each intermediate heat exchanger feeds a dedicated steam generator and has a dedicated drain down tank and dedicated electric induction pump. Hence in the event of a problem any single heat transport loop can be shut down while the other heat transport loops remain operational.
 

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SPECIAL EQUIPMENT:
The 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.
 

PIPE CONNECTIONS:
The hot secondary liquid sodium is directly connected to the adjacent steam generator. Flexible air and argon bellow wall seals are required at locations where the secondary sodium pipes pass through the inner reactor enclosure wall to accommodate thermal expansion/contraction. Under ordinary operation the reactor power is modulated by controlling the secondary sodium circulation rate via the induction pumps. This control methodology causes significant pipe thermal expansion/contraction.

The secondary sodium service pipes and the induction pump must be separately supported with threaded hardware so that these pipes remain in correct position when an intermediate heat exchanger is disconnected.
 

INTERMEDIATE HEAT EXCHANGER WEIGHT:
Shell= _______ The weight of the tubes in each intermediate heat exchange bundle is given by:
Pi [(0.50 inch)^2 - (0.37 inch)^2][1 / 4] X (0.0254 m /inch)^2 X 6.1 m / tube X 1680 _______tubes X (8000 kg_____ / m^3)
= 4621.36 kg

The weight of each intermediate heat exchange bundle manifold is estimated to be ~ 2 tonnes_____.

End cap = ________

Hence the total intermediate heat exchange bundle weight including its service pipe stubs will likely be about 9 ______tonnes.
 

INTERMEDIATE HEAT EXCHANGER TUBE OPEN CROSS SECTIONAL AREA:
The open cross sectional area of one heat exchange bundle on the tube side is:
Pi (0.37 inch / 2)^2 / tube X (.0254 m / inch)^2 X 823 tubes_____ / bundle
= _______ m^2

By comparison the service pipe open area is:
Pi (______ inch / 2)^2 X (.0254 m / inch)^2 = ________ m^2
which is acceptable due to increased viscous forces within the heat exchange tubes.
 

INDUCTION PUMP:
The induction pump must be sized to overcome the flow pressure head in the secondary sodium piping. Note that these pumps must be located on the low temperature return pipes and must be physically near the bottom of the secondary sodium loop to ensure positive suction head.

The induction pump operates by inducing a circular current in the liquid sodium. 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.
 

SECONDARY SODIUM CIRCULATION PUMPING POWER:
The secondary liquid sodium acceleration power is:
[(flow pressure head) X (volumetric flow rate) / (flow cross sectional area)] = ______

The induction pumps are unlikely to be more than 10% efficient.

Each loop needs at least ____ of mechanical circulating energy. If the induction pump is 10% efficient each intermediate loop needs:
5 X 0.6 kWe = 3.0 kWe
of pumping electric power. Hence the total secondary sodium circulation pumping electricity requirement is at least:
32 X 3.0 kW = 96 kWe_________

Allowing for flow pressure drops across the intermediate heat exchangers and the steam generators the total liquid sodium intermediate circulation pumping power will likely be of the order of 200 kWe._________
 

GASKET CONSTRAINT:
A major constraint on the FNR design is gasket properties. This FNR operates at too high a (temperature X pressure) product for use of elastomeric gaskets. Soft metal gaskets must be used. Such gaskets do not tolerate pipe misalignment or manifold distortion. Hence gasketed mechanical joints need optical precision fabrication. This precision may be essential for heat exchange bundle manifold fabrication. All the heat exchange bundle manifolds bottom and top halves are sealed with soft metal gaskets and bolted and then edge welded all around. The weld is mechanically and safety relieved by the flange bolts.
 

SECONDARY LIQUID SODIUM FLOW:
Under ordinary operation the reactor power is controlled by modulating the secondary sodium flow rate. The induction type circulation pumps are located in the cooler secondary sodium return pipes where there is always adequate suction head.

Each intermediate heat exchanger is piped to a dedicated steam generator with the secondary sodium circulation pump on the lower cool side of the loop. This arrangement elijminates the requirement for sodium valves. The liquid sodium injection/removal port to the dump tank relies on argon pressure wich is controlled by external low temperature argon valves. To charge the loop with liquid sodium it is injected into the lowest point in the loop via the drain tube and the system top pipe is vented to the pool space.

This arrangement requires a reliable valves on small argon pipes connected to the drain down tank that either vent the drain down tank to the argon atmosphere or connect pressurized argon to drive liquid sodium out of the drain down tank. Similarly there are complementary reliable valves to control argon flow to and from the top of the secondary heat exchange loop.

This configuration balances flows, optimizes heat transfer and minimizes thermal stresses. The standard piping connection arrangement for each high pressure secondary sodium circuit starting at the 12 inch induction pump: 1 X 12 inch straight pipe, 1 X 12 inch 90 degree elbow, the intermediate heat exchanger lower manifold, the intermediate heat exchange tubes, the intermediate heat exchanger upper manifold, 1 X 12 inch straight pipe, 1 X 12 inch 90 degree elbow, one 12 inch horizontal straight pipe section, 1 X 12 inch 90 degree elbow, 1 X 12 inch straight pipe section, the steam generator upper manifold, the steam generator tubes, the steam generator lower manifold, 1 X 12 inch straight pipe section, 1 X 12 inch to 16 inch adapter, 1 X 16 X 16 X 16 inch tee, 1 X 16 inch to 6 inch adapter down to a high pressure dump tank, and a 16 inch connection to the 16 inch induction pump flow tube. There is one small drain/fill valve for each heat exchange system. This arrangement permits practical and safe identification, isolation, draining, replacement and refilling of any defective heat transport loop component.The pipes must have sufficient positioning play to allow for thermal expansion-contraction and possible earthquake related movement.
 

INTERMEDIATE SODIUM PRESSURE CHANGE DUE TO NATURAL CIRCULATION:
In normal full load reactor operation the reactor produces 875 MWt of heat. When the chain reaction is off the reactor may still produce as much as:
0.08 X 875 MWt = 70 MWt
of fission product decay heat.

Hence natural circulation of the secondary sodium with the steam generators at atmospheric pressure should run at over 8% of the pumped circulation rate.

The natural circulation rate will be primarily limited by the temperature difference between the rising leg and the falling leg and by the viscous flow pressure drop across the intermediate heat exchange bundle and the steam generator bundle. Thus these pressure drops need to be quantified.

The volumetric TCE of liquid sodium is 240 ppm / deg C. Hence if there is a 100 degree C temperature difference between the rising and falling legs the change in sodium density is:
.967 kg / lit X 240 X 10^-6 / deg C X 1000 lit / m^3 X 100 deg C = 0.967 X 24 kg / m^3

Assume an elevation difference of 10 m. Then the corresponding differential pressure is:
0.967 X 24 kg / m^3 X 10 m X 9.8 m / s^2 = 2274 Pa

In an emergency when the steam generator is flooded with water at a low pressure the temperature difference between the rising leg and the falling leg can rise to 300 degrees C implying that a theoretical maximum differential pressure of about:
2274 Pa X 3 = 6823 Pa is available. However, the consequent thermal stress might easily damage the steam generator.

We need to compare these pressure drops to the viscous pressure drop across the intermediate heat exchanger and steam generator tube bundles at 1 / 10 of normal flow.
 

CALCULATE SECONDARY SODIUM VISCOUS PRESSURE DROP AT SUFFICIENT NATURAL CIRCULATION TO REMOVE FISSION PRODUCT DECAY HEAT:
An important issue with the intermediate heat exchange bundles is their ability to remove fission product decay heat by natural circulation. In natural circulation the liquid sodium flow rate is low and laminar, so the heat transfer characteristics are different from when the secondary loop is pumped. It is necessary to have a sufficient number of intermediate heat exchange tubes to allow the required natural circulation and laminar flow limited heat transfer. The viscosity of the sodium must be taken into account.
 

The following equations derived on the web page titled FNR PRIMARY SODIUM FLOW can be used to find the natural circulation volumetric fluid flow Fv per round coolant flow channel.
Fv = {Pi Pg Ro^4 / [Muv Zo (N + 2)(N + 4)]}BR> where:
Pi = 3.14159
Pg ~ 1000 Pa
Ro = (0.37 inch / 2) X (0.0254 m / inch) = 0.004699 m
Muv = 3 X 10^-4 N-s / m^2
(N + 2) = Ro [(Rhos Pg) / 2]^0.25 [1 / [Muv Zo]^0.5]
where:
Zo = 6.0 m
Rhos = 849.4 kg / m^3

Numerical substitution gives:
(N + 2) = Ro [(Rhos Pg) / 2]^0.25 [1 / [Muv Zo]^0.5]
= 4.699 X 10^-3 m [(849.2 kg / m^3) (1000 kg m /s^2 m^2) / 2]^0.25 [1 / [(3 X 10^-4 N^-s / m^2)(6 m)]^0.5]
= 4.699 X 10^-3 m [25.5267 kg^0.5 / s^0.5 m] [ 1 / [4.24264 X 10^-2 (kg m s /s^2 m)^0.5]]
= 2.8272482 kg^0.5 s-0.5 kg^-0.5 s^0.5
= 2.8272482

Hence the secondary sodium natural circulation flow Fv through each tube is given by:
Fv = {Pi Pg Ro^4 / [Muv Zo (N + 2)(N + 4)]} = {3.14159 (1000 N / m^2)(0.004699 m)^4 / [(3 X 10^-4 N - s / m^2) (6 m) (2.8272)(4.8272)]}
= {3.14159 (1000)(487.55294 X 10^-12 m^2 / [(245.654277 X 10^-4 s / m)]}
= 6.23515 X 10^-5 m^3 / s

With 1023 tubes_________ / bundle the secondary sodium natural circulation flow rate is:
1023 tubes/bundle X 6.23515 X 10^-5 m^3 / s-tube = 0.06378 m^3 / s which is faster than the minimum required natural circulation rate.
 

Note that there is enough heat stored in the liquid sodium pool to sustain electricity production for several minutes after the reactor chain reaction is shut down. The situation being addressed here is one of induction pump off and chain reaction shutdown but continued reactor heat production due to fission product decay.
 

SECONDARY SODIUM VOLUME:
The volume of each secondary sodium circuit can be estimated by assuming that everywhere along that circuit the cross sectional area is approximately the same as the cross sectional area of a 12.75 inch___ diameter pipe.

Thus the minimum pipe length equivalents are:
Intermediate heat exchanger tibes = 6 m
Steam generator tubes = 6 m
4 Manifolds = ???? Horizontal pipes = 2 X (2 m) = 4 m
Vertical pipes = 4 X 0.5 m = 2 m

Hence total equivalent pipe length = 30 m

System volume = Pi (6.4 inch)^2 X 30 m X (.0254 m / inch)^2 = 2.49 m^3

Required secondary sodium drain down tank volume = _______

Thus the total secondary sodium volume is about:
56 X 2.49 m^3______ = 79.70 m^3_______
 

CONSTRUCTION:
Each intermediate heat exchanger has two tube sheet forgings and two end cap forgings that are similat to those used by the steam generator. However, the 24 inch (610 mm) outside diameter shell wall of the steam generator is much thicker than the 24 inch (610 mm) outside diameter shell wall of the intermediate heat exchanger. The intermediate heat exchanger has 18 inch diameter pipes going to the primary liquid sodium pool. The high pressure secondary sodium piping is 12.75 inch OD. The drain down tank is formed from 24 inch diameter pressure pipe. It has an external electric heater, similar to the heating element on an electric domestic hot water tank, for startup sodium melting.
 

INSTALLATION:
The intermediate heat exchangers are installed in heat exchange galleries by lowering using an overhead crane. Each unit rests on a column with a jack for precise height adjustment. The height is adjusted for accurate alignment with the pre-cut primary sodium pipe holes in the reactor enclosure wall. Once in place the tops of the units are horizontally stabilized to all four concrete walls. Each heat exchange gallery has an internal length of 12.5 m and an internal width of 8.5 m. Each intermediate heat exchanger-steam generator pair is allocated a gallery wall length of 1.5 m. There is 0.5 m of wall clearance at each end of the upper gallery. The intermediate heat exchanger-steam generator center to center spacing is 4 m. Adjacent pairs are staggered so that the smallest wall clearance is 0.5 m. Pipes to the primary sodium pool go straight through the pool enclosure wall before bending to reach the desired positionon the sodium pool perimeter. Pipes carrying secondary sodium go directly to the adjacent steam generator. The secondary sodium return pipe has an induction pump mounted on it.

Each heat exchange gallery has a basement level where the induction pumps, induction pump power supples and the drain down tanks are located. Equipment and personnel access to the heat exchange gallery basement level is via a stair well far from the airlock. Drain down tanks are lowered by crane from above.

An important issue in the heat exchange gallery basement is separation of water and sodium drips. Water is only likely to leak near the outside wall. Elsewhere there could be sodium drips. A cement ridge should be provided across the basement floor to separate these two accumulations. The water sump and the water sump pump should be located near the outside wall.

As a rule of thumb electrical equipment should be mounted on the inside wall which is less subject to water penetration. There will need to be a large air vent in the access stair well end wall for air cooling.

The heat exchange gallery basement water sump pump will likely need to drain into a near grade level storm sewer. It would be better if it drained into the facility bottom drain at 16 m below grade.
 

This web page last updated October 13, 2020

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