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XYLENE POWER LTD.

FNR INTERMEDIATE HEAT EXCHANGER

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

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.

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.

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

Thus in the intermediate heat exchanger 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.

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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.
 

In spite of the protective 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. When the freeze valve is open the drain down tank also acts as an expansion tank and attenuates any pressure pulses in the secondary liquid sodium.
 

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____

INTERMEDIATE HEAT EXCHANGER CONSTRUCTION:
This arrangement also means that the intermediate heat exchanger tubes and tube manifolds must be strong enough to withstand the longitudinal force exerted by the secondary sodium. In the event of an intermediate heat exchange tube wall failure the intermediate sodium contained in the failed secondary sodium circuit will flow into the primary sodium pool.
 

The contemplated intermediate heat exchanger is realized using a 20 foot lengths of (1 / 2) inch OD steel tubes. These tubes are available with sufficient wall thickness (0.065 inch) to safely withstand the maximum steam pressure on the shell side of the steam generator. The tubes terminate in cast end manifolds.

Each 20 foot long X 2 foot outside diameter intermediate heat exchanger will accept: over 625 X 0.5 inch OD tubes on 0.70 inch staggered grid centers. Within each such tube bundle there is a heat exchange area of:
625 tubes X 230 inches / tube X Pi X .435 inch = 196,447 inch^2
= 126.74 m^2

The corresponding heat flow rate per steam generator bundle limited by Inconel 600 conductivity is: 20.9 Wt / m-deg K X 126.74 m^2 X (1 / .065 inch) X (1 inch / .0254 m) = 1,604,400 Wt / deg K
= 1.604 MWt / deg K

Thus temperature drop across the heat exchange bundle tube wall is:
(875 MWt / 56) / (1.604 MWt / deg K)
= 9.741 deg C
 

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MANIFOLD END CAPS:
The heat exchanger manifolds ans end caps may have to be cast from Haynes 617 Alloy
 

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 high pressure intermediate sodium enters the steam/ water cavity where it generates hydrogen. The loss of liquid sodium in the secondary sodium circuit is detected and triggers a vent of steam/hydrogen 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 intermediate 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

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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.
 

INTRODUCTION:
This web page deals with FNR intermediate heat exchanger tubes and FNR Steam Generator Tubes. The physical properties of these tubes dictate many aspects of FNR design. A major constraining issue is the tolerable level of combined thermal stress and internal pressure stress in the heat exchange tubes which normally operate in the temperature range 290 degrees C to 500 degrees C.

It is shown that due to best performance under severe thermal stress the best heat exchange tube material for both the intermediate heat exchangers and the steam generators is likely Inconel 600.
 

MATERIAL PROPERTIES:
Define:
TC = thermal conductivity
TCE = thermal coefficient of expansion
DeltaT = temperature drop across steel tube wall
Y = (stress / strain) = Young's modulus
Sy = yield stress

Key material properties are set out in the following table:
PROPERTY316LHT-9D915/15TiINCONEL
Density7966 kg / m^38200 kg / m^38430 kg / m^3
TC @ 500 C15 W / m-K26.2 W / m-K20.2 W / m-K20.9 W / m-K
TCE @ 500 C18 X 10^-6 / K15 X 10^-6 / K13 X 10^-6 / K15.1 X 10^-6 / K
Y @ 25 C202 GPa---207 GPa
Y @ 250 C, no rad.-2000 GPa----
Y @ 250 C, with rad.2000 GPa----
Y @ 350 C, no rad860 GPa
Y @ 350 C, with rad1200 GPa
Bulk Y @ 500 C120 Gpa135 GPa--
Sy @ 25 C, no rad.291.3 MPa---630 MPa550 MPa
Sy @ 250 C, no rad.600 MPa-570 MPa-
Sy @ 250 C, rad900 MPa--
Sy @ 350 C, no rad.420 MPa560 MPa-
Sy @ 400 C, rad600 MPa to 900 MPa--
Sy @ 465 C, no rad725 MPa-530 MPa-
Sy @ 460 C, with rad520 MPa--
Sy @ 500 C, no rad167 MPa400 MPa to 550 MPa510 MPa579 MPa
Sy @ 500 C, with rad450 MPa to 600 MPa--
-------

INTERMEDIATE HEAT EXCHANGE TUBES:
The optimum choice of heat exchange tube material for an FNR is a complex property tradeoff. With respect to the FNR design developed on this web site natural circulation of the primary liquid sodium is used to achieve mechanical simplicity. However, with natural circulation of the primary liquid sodium the liquid sodium at the bottom of the primary liquid sodium pool operates at about 320 degrees C and the liquid sodium at the top of the liquid sodium pool operates at about 480 degrees C. Various parts of a heat exchange tube normally operate in the temperature range 310 C to 488 C. The heat exchange tubes must safely accommodate initial fuel bundle insertion in the FNR when the sodium inside the fuel tube is initially solid.

Another practical consideration in choosing the heat exchange tube material is its workability. Each FNR has ~ 70,000 heat exchange tubes that must be automatically fabricated, assembled and tested.

The heat exchange tube alloy must be chemically compatible with Na, H2O, UO2, U, Pu, Zr, fission products, transuranium actinides from 20 degrees C to 530 degrees C.
 

PRESSURE AND THERMAL STRESSES:
Due to the internal pressure an intermediate heat exchange tube wall is under tension. The material pressure stress is partially balanced by the radial heat flux changes the stress distribution. Net stress will over time cause intermediate heat exchange tube material creep and hence heat exchange tube diameter increase.
 

316L is a high performance austenitic stainless steel tube alloy that has been ASME approved for use in fired pressure vessels for over 30 years. 316L features good weldability. According to the Euporean Stainless Steel Development Association the term 316L refers to steels that comply with:
<0.030% C + <1.00% Si + <2.00% Mn + <0.045% P + <0.015% S + <0.11% N
+ {16.5% Cr to 18.5% Cr + 2.00% Mo to 2.500% Mo + 10% Ni to 13% Ni + Fe}
or + {17.0% Cr to 19.0% Cr + 2.50% Mo to 3.00% Mo + 12.5% Ni to 15% Ni + Fe}
or
+ {16.5% Cr to 18.5% Cr + 2.50% Mo to 3.00% Mo + 10.50% Ni to 13.00% Ni + Fe}
 

FOR 316L STAINLESS STEEL HEAT EXCHANGE TUBES:
Thermal Stress:
(DeltaT)
= (Sy)(2) / [(TCE) Y]
= [24,400 psi(2) X (101,000 Pa / 14.7 psi)] / [ (17.5 X 10^-6 / deg C) X (202 X 10^9 PA)]
= [48.8 X 101 X 10^12 deg C] / [14.7 X 17.5 X 2.02 X 10^11]
= 94.80 deg C

For a conservative safe design the maximum thermal stress and hence the maximum operating temperature differential should be reduced by a factor of three to: 31.60 deg C

However, there is also differential pressure stress. If the stresses are to be equally divided between differential temperature and differential pressure the maximum differential temperature across the tube wall further decreases to 15.8 C.

Thus the maximum operating heat flux through the 316L stainless steel tubes is:
15.8 deg C X 15 W / m-deg C / (.065 inch X .0254 m / inch) = 143,549.4 W / m^2

The intermediate heat exchange tube area is:
Pi X (.500 inch) X (.0254 m / inch) X 6.0 m / tube X 32 bundles X 1084 tubes / bundle
= 8304 m^2

Hence the corresponding maximum possible reactor thermal power is:
143,549 W / m^2 X 8304 m^2 = 2092,854,595 Wt
= 1,192.0 MWt

In reality the maximum reactor power will be limited by the liquid sodium flow between the reactor core fuel tubes.

The corresponding allowable differential pressure P is given by:
P (.37 inch) = (Syp / 6) 2 (.065 inch)
or
P = (Syp / 6)(0.13 inch / 0.37 inch)
= 30,000 psi (.05855)
= 1756.7 psi
= 119.5 bar
= 12.07 MPa
 

OTHER TUBE ALLOYS CONSIDERED:
316 According to Gimondo 316 consists of:
{Fe + 0.05% C + 17% Cr + 2.0% Mo + 0.6% Si + 1.8% Mn + 13% Ni + 20 ppm B}
 

316 Ti is an austenitic stainless steel alloy described by Gimondo as consisting of:
{Fe + 16% Cr + 2.5% Mo + 14% Ni + 0.6% Si +1.7% Mn + 0.05% C + 0.4% Ti +0.03% P}
 

D9 is a titanium stabilised austenitic stainless steel Indian alloy described by Leibowitz and Blomquist as consisting of the weight percentages:
{65.96% Fe + 13.5% Cr + 2.0% Mo + 15.5% Ni + .04% C + 2.0% Mn + 0.75% Si + 0.25% Ti}
and described by Banerjee et al as:
{Fe + 14.7% Cr + 2.2% Mo + 14.9% Ni + .05% C + 1.3% Mn + 0.65% Si + 0.18% Ti
+ <.05% Cu + <.07% Nb + .045% V + .03% Co + <.034% Al + <.004% Sn + .005% W + <.04% N + .008% P + .005% S + <.006% As}
and is described by Karthik et al as:
{Fe + 13.5% to 14.5% Cr + 2% Mo + 14.5% to 15.5% Ni + .035% to .05% C + 1.65% to 2.35% Mn + 0.5 to 0.75% Si + 0.2% Ti}
and is described by Gimondo as consisting of:
{Fe + 13.5% Cr + 2.0% Mo + 15.5% Ni + .04% C + 2.0% Mn + 0.75% Si + 0.25% Ti}

The alloy D9 features a higher creep rupture strength, a lower creep rate and a lower rupture ductility than 316L.
 

15/15 Ti (12R72) is an austenitic stainless steel European alloy described by Gimondo as consisting of the weight percentages:
{Fe + 15% Cr + 1.2% Mo + 15% Ni + 0.10% C + 1.5% Mn + 0.6% Si + 0.4% Ti + 0.03% P + 50 ppm B}

15/15 Ti (12R72) has an approximate fast neutron dose limit of 120 dpa. It has a Larson Miller parameter of 23.8 at 100 MPa.
 

OTHER ALLOY PROPERTIES:
9Cr - 1 Mo steel has a well documented creep rupture life.

T91 is a ferritic-martensitic steel with Larsen Miller parameter 21.5 at 100 MPa.

A major issue with Austenitic stainless steel such as 316 used at 420 C is that under prolonged fast neutron exposure it swells as much as 25% whereas under the same neutron exposure ferritic steels expand < 1%. This swelling will reduce the flow of cooling liquid sodium through the reactor core.
 

HEAT EXCHANGE TUBES:
Inconel 600 is a high nickel alloy that maintains its yield stress rating at high temperatures and hence is widely used in high temperature heat exchangers where there may be both substantial pressure differences and high thermal stress. It is described by American Special Metals and Rolled Alloys Inc. as:
> 72% Ni (+ Co) + 14.0% to 17.0% Cr + 6.00% to 10.00% Fe + < 0.15% C + < 1.0% Mn + < 0.015% S + < 0.50% Si + < 0.50% Cu

Inconel-600 is only used in heat exchangers that are outside the neutron flux. The inconel 600 must be chemically compatible with Na and H2O at 100 to 500 degrees C.
 

FOR INCONEL 600:
(DeltaT) = (Sy)(2) / [(TCE) Y]
= [579 MPa (2)] / [ (15.1 X 10^-6 / deg C) X (207 X 10^9 Pa)]
= [1158 X 10^6 Pa deg C] / [15.1 X 207 X 10^3 Pa]
= 370.5 deg C

For a conservative safe design the maximum stress and hence the maximum operating temperature differential should be reduced by a factor of three to: 123.5 deg C

In order to allow for half the allowable stress being due to internal pressure further reduce the operating temperature differential by another factor of two to 61.75 degrees C.

Thus the conservative operating heat flux through the Inconel 600 tubes of the primary to secondary heat exchanger is:
61.75 deg C X 20.9 W / m-deg C / (.065 inch X .0254 m / inch) = 781,693 w / m^2

The heat exchange tube surface area is:
Pi X (.500 inch) X (.0254 m / inch) X 5.5 m / tube X 1084 tubes / bundle X 32 bundles = 7612 m^2

The maximum allowable internal gas pressure causes a hoop stress of:
(Sy / 6) = 24,400 psi / 6
= 4067 psi.
(Max Pressure) X (.500 inch - .130 inch) X L = 4067 psi X 2 x .065 inch X L
or
Maximum pressure = 4067 psi X .130 inch / .37 inch
= 1429 psi
= 97.2 bar
 

STRESS ISSUES:
Another major constraining issue is the combined thermal stress and internal pressure stress in the tubes which form the intermediate heat exchanger. In addition to internal pressure the intermediate heat exchanger has a significant temperature differential across the tube wall. This temperature differential can potentially lead to high thermal stress at the point where the cool secondary return sodium is first heated by the primary liquid sodium. This problem is minimized by keeping the primary liquid sodium temperature stratified.

One of the issues with Inconel is long term creep. This issue is particularly important in the intermediate heat exchanger.

In the steam generator the material stress due to differential pressure across the tube wall is relatively small because the liquid sodium pressure is controlled to track the steam pressure. However, the thermal stress can be very large at the point where inlet water to the steam generator is first heated by liquid sodium that is on its way back to the intermediate heat exchanger.
 

PRESSURE AND THERMAL STRESSES:
Due to the internal pressure the inside of an intermediate heat exchange tube wall is under tension. The radial heat flux places the inside of the tube wall under compression and the outside of the tube wall under tension. Net stress will over time cause intermediate heat exchange tube material creep and hence cause the heat exchange tube diameter increase.
 

CREEP AND THERMAL STRESS:
Another major constraining issue is the combined thermal stress and internal pressure stress in the tubes which form the intermediate heat exchanger. In addition to internal pressure the intermediate heat exchanger has a significant temperature differential across the tube wall. This temperature differential can potentially lead to high thermal stress at the point where the cool secondary return sodium is first heated by the primary liquid sodium. This problem is minimized by keeping the primary liquid sodium temperature stratified.

One of the issues with Inconel is long term creep. This issue is particularly important in the intermediate heat exchanger. To minimize the effect of long term creep on primary sodium flow the tubes in the intermediate heat exchanger are arranged in a square lattice rather than a staggered lattice and the tube center to center distnace is made 1.00 inch.

In the steam generator the material stress due to differential pressure across the tube wall is relatively small because the liquid sodium pressure is controlled to track the steam pressure. However, the thermal stress can be very large at the point where inlet water to the steam generator is first heated by liquid sodium that is on its way back to the intermediate heat exchanger.
 

TUBE REQUIREMENT:
Let N be the required minimum number of tubes.
Within each heat exchange tube bundle there is a heat exchange area of:
N tubes X 230 inches / tube X Pi X (.500 inch - 0.065 inch) = N X 314.316 inch^2
= N X 0.20278 m^2

The corresponding heat flow rate per bundle limited by Inconel 600 conductivity is: 20.9 Wt / m-deg K X N X .20278 m^2 / tube X (1 / .065 inch) X (1 inch / .0254 m)
= 2567.0 N Wt / tube deg K
 

STEAM GENERATOR :
Assume that in the steam generator there is one central tube surrounded by 15 hexagonal rings of tubes. Then the total number of tubes for such a hexagonal array is:
1 + 6 + 12 + 18 + 24 + 30 + 36 + 42 + 48 + 54 + 60 + 66 + 72 + 78 + 84 + 90
= 7 + 7 (102)
= 715 tubes

Now assume corner clipping to approximate a circle:
The 13th ring loses 1 X 6 = 6
The 14th ring loses 5 X 6 = 30
The 15th ring loses 9 X 6 = 54

Hence the total number of tubes lost is:
6 + 30 + 54 = 90

Hence the number of tubes remaining for use in the steam generator is:
715 - 90 = 625 tubes

The corresponding heat flow rate per steam generator limited by Inconel 600 conductivity is:
= 2567.0 N Wt / tube deg K X 625 tubes = 1,604,375 Wt / deg K

Now assume a staggered lattice tube center to tube center distance space of 0.700 inches. On the flat hexagon faces the inter-ring distance is:
0.7000 inch X 3^0.5 / 2 = 0.6062177826 inches

The required shell inside diameter is slightly greater than:
31 X 0.6062177826 inches = 18.79275 inches

For the steam generator with a schedule 160 shell the available shell inside diameter is:
610 mm - 2(59.54 mm)
= 490.92 mm /(25.4 mm / inch) = 19.32756 inch

That dimensional choice allows for a
(19.32756 inch - 18.79275 inch) / 2
= 0.2674 inch
= (1 / 4) inch clearance around the tube bundle to allow for shells and tubes with non-ideal dimensions.

The area of a 0.500 inch diameter hole is:
Pi (0.25 inch)^2 = 0.1963495 inch^2

The area of 625 holes is:
625 X 0.1963495 inch^2 = 122.718 inch^2

The steam generator end face area = Pi (19.33 inch / 2)^2
= 293.463 inch^2

Hence the loss of tube sheet material strength due to tube sheet boring is:
122.718 / 293.463 = 0.411817
= 41.18%

The loss of inside shell cross sectional area for fluid flow is also 41.8%.

The inside shell open area is:
(100% -41.8%) X 293.463 inch^2
= 170.80 inch^2
= Pi (54.365 inch^2)
= Pi (7.373 inch)^2
= Pi (14.746 inch / 2)^2
which requires 16 inch diameter pipe

Thus with a thick (Schedule 160 pipe) shell the maximum number of tubes with a 0.70 inch staggered grid is 625 tubes and the connected steam pipes must be 16 inch nominal diameter.
 

INTERMEDIATE HEAT EXCHANGER:
With a shell formed from 24 inch diameter Schedule 40 pipe the shell inside diameter is:
610 mm - 2 (17.48 mm) = 575.04 mm

The increase in shell inside diameter as compared to a steam generator is:
575.04 mm - 490.92 mm = 85.88 mm

Each additional tube ring requires:

Two more rings of tubes will require:
2 (1.400 inches) = 2.8 inches more shell diameter. If the shell is Schedule 40 pipe the available additional shell inside diameter is:
85.88 mm / (25.4 mm / inch) = 3.381 inch
Hence, as compared to a stem generator there is space for two more rings of tubes.

The number of tube positions in 17 complete hexagonal rings would be:
1 + 6 + 12 + 18 + 24 + 30 + 36 + 42 + 48 + 54 + 60 + 66 + 72 + 78 + 84 + 90 + 96 + 102
= 7 + 8 (114)
= 7 + 912
= 919 tube positions

Due to corner rounding this number of tube positions will be reduced by:
6 (1) + 6 (5) + 60
= 96 tubes

Hence an intermediate heat exchanger contains:
919 - 96 = 823 tubes

Then for the intermediate heat exchanger the heat transfer rate across the tube walls is:
823 tubes X 2567.0 Wt / tube deg C = 2,112,641 Wt / deg C

Thus at a FNR thermal power of 875 MWt the temperature drop across the intermediate heat exchange tube metal is:
875 MWt / [(2.112641 MWt / deg C -exchanger) X 56 exchangers] = 7.396 deg C

For the intermediate heat exchanger the end face cross sectional area is:
Pi (575.04 mm / 2)^2 X (1 inch / 25.4 mm)^2
= Pi (11.3196 inch)^2

For the intermediate heat exchanger the tubes reduce the inside shell cross sectional area by:
823 tubes X Pi (0.500 inch / 2)^2
= Pi (51.4375 inch^2)
= Pi (7.172 inch)^2

Thus for the intermediate heat exchanger the in-shell cross sectional area is:
Pi (11.3196 inch)^2 - Pi (7.172 inch)^2
= Pi [128.133 inch^2 - 51.4357 inch^2]
= Pi [76.6973 inch^2]
= Pi [8.7577 inch]^2
= Pi [17.515 inch / 2]^2

Hence the primary sodium flow connections to the intermediate heat exchangers must be the equivalent in cross sectional area to 18 inch nominal diameter pipes..
 

MANIFOLD OUTSIDE DIAMETER:
Unless the intermediate heat exchangers are radially staggered There is a hard limit on the intermediate heat exchanger manifold outside diamater of:
18 m (Pi) / 60 = 0.942478 m
= 37.10 inch
which allows for a 6 inch wide rim with 1.1 inches for clearance. It would be better to radially stagger the intermediate heat exchangers to allow wider rims.

This web page last updated June 9, 2020

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