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**INTERMEDIATE HEAT EXCHANGE TUBE BUNDLE:**

The purpose of an Intermediate Heat Exchange Bundle is to transfer heat from the FNR primary sodium into higher pressure FNR secondary sodium. The 56 intermediate heat exchange tube bundles are immersed in the primary liquid sodium. These heat exchange tube bundles isolate the radioactive primary liquid sodium from the non-radioactive secondary liquid sodium. The intermediate heat exchange tube bundles also serve as a barrier to other radioactive species in the event of a fuel tube leak. In the event of an intermediate heat exchange bundle leak the higher pressure of the secondary sodium ensures that radioactive species do not migrate from the primary sodium into the secondary sodium.

**INTERMEDIATE HEAT EXCHANGE BUNDLES:**

To attain the desired temperature distribution in the intermediate heat exchanger bundles the secondary sodium mass flow rate must be the same as the primary sodium mass flow rate. However, the primary sodium flow cross sectional area is larger so the primary sodium linear descent velocity is smaller.

The maximum outside diameter of the intermediate heat exchange manifolds is limited to:

**38 inches**

so that 56 of them will fit in the available space on an 18 m diameter circle in the primary sodium pool.

The intermediate heat exchange bundles are in nearly fixed positions with respect to the concrete enclosure. When the system is warm there is about a 0.15 m gap between the cool sodium pipe insulation and the primary sodium inside tank wall. As the system cools this gap slowly shrinks to zero.

**INTERMEDIATE HEAT EXCHANGER TUBE OPEN CROSS SECTIONAL AREA:**

The cross sectional area of the rising secondary sodium in an intermediate heat exchnge bundle is:

800 tubes X [Pi (0.37 inch / 2)^2] / tube

= Pi [27.38 inch^2]

= Pi [5.2326inch]^2

= Pi [10.465 inch / 2]^2

= .0555 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.

**INTERMEDIATE HEAT EXCHANGE BUNDLE 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.

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 TUBES:**

Assume that the intermediate heat exchange bundle tubes are 0.500 inch OD, 0.065 inch wall 316 SS. Then tube ID is:

ID = 0.500 inch - 2(0.065 inch)

= 0.37 inch

Let Pm be the maximum working pressure of these tubes. Then:
Pm (0.37 inch) = 2 (.065 inch)(39 MPa)

or

**Pm** = 2 (.065 inch)(39 MPa) / 0.37 inch

= **13.7 MPa**

Thus the tube wall thickness sets the maximum allowable sodium working pressure at **13.7 MPa**.

Note that this is 3X greater than the 4.6 MPa maximum pressure set by schedule 80 pipe and fittings. It may be prudent to use tube with a smaller wall thickness._____

**INTERMEDIATE HEAT EXCHANGER TUBE OPEN CROSS SECTIONAL AREA:**

The cross sectional area of the rising secondary sodium in an intermediate heat exchnge bundle is:

800 tubes X [Pi (0.37 inch / 2)^2] / tube

= Pi [27.38 inch^2]

= Pi [5.2326inch]^2

= Pi [10.465 inch / 2]^2

= .0555 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.

**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.

**SECONDARY SODIUM PRESSURE DROP ACROSS THE INTERMEDIATE HEAT EXCHANGE BUNDLE:**

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 sodium-salt heat exchangers the total liquid sodium intermediate circulation pumping power will likely be of the order of 200 kWe._________

**PROCEDURE FOR INTERMEDIATE HEAT EXCHANGE BUNDLE REPLACEMENT:**

Replacing an intermediate heat exchanger involves the following steps:

a) Cool down the secondary sodium to 120 deg C;

b) Transfer the secondary sodium in the defective heat transport loop into the loop dump tank;

Upstream from the induction pump is a vertical axis tee with a horizontal branch for 16 inch OD pipe to permit complete drainage of the liquid sodium contained within the induction pump. The lower port on this tee goes to the dump tank.
c) Disconnect both secondary sodium service pipes at the flanged connections;

d) Immediately blank off the disconnected pipes;

e) Use a crane to lift the defective heat exchange bundle clear of the secondary sodium pipes and into an airlock;

f) Transfer the defective heat exchanger to a service vehicle;

g) Lift a replacement intermediate heat exchanger into place using the same air lock and crane;

h) Rotate the new heat exchange bundle so that its connection flanges align with the secondary sodium service pipes;

k) Make pipe connections with appropriate high temperature rated metal gaskets. Use a laser alignment tool;

l) Test that the system holds argon pressure.

m) Insulate the piping;

n) Transfer secondary liquid sodium from the dump tank back into the secondary heat transport loop;

**INLET PIPE STRESS RELIEF:**
The temperature of the secondary sodium approaching the intermediate heat exchange inlet is about 330 degrees C. The temperature of the primary sodium near this inlet point may be over 400 degrees C. To mitigate thermal stress in the secondary sodium inlet pipe this pipe should be sleeved to reduce material thermal stress.

**INTERMEDIATE HEAT EXCHANGE BUNDLE MANIFOLD SIZE CONSTRAINTS:**

The intermediate heat exchange tube bundle centers are located on an 18 m diameter circle coaxial with the 20 m diameter primary sodium pool.

The theoretical maximum outside diameter of the intermediate heat exchange manifolds is limited to:

Pi (18 m) / 56 = 1.01 m = 39.756 inch

In order to allow for fabrication and positioning tolerances the Intermediate Heat Exchange Bundle manifold OD is chosen to be 38.0 inches. We want a manifold ID of 24 inches, which leaves:

(38 inch - 24 inch) / 2 = 7 inches

of which:

manifold side wall thickness = 1.5 inches:

gasket seal width = 1 inch

bolted rim width = 4.5 inch

Manifold side wall ID = 24 inch

Manifold side wall OD = 27 inch

To conserve material the manifold top is 24 inch OD disk which fits inside the manifold wall and the manifold cover flange is:

ID = 27 inch

OD = 38 inch

which fits outside the manifold wall.

As shown on the web page titled: FNR Secondary Sodium Heat Transport System the maximum working pressure of the secondary sodium is 4.6 MPa.

**HOOP STRESS:**

Let Sh = hoop stress on manifold side walls.

Sh X 2 X 1.5 inch = 4.6 MPa X 24 inch

or

Sh = 4.6 MPa X 8

= 36.8 MPa.

As shown on the web page titled: FNR Secondary Sodium Heat Transport System if the material is 316 SS the maximum allowed material working stress at 800 degrees K is 39 MPa, so the hoop stress constraint is met.

**BOLT STRESS;**

The manifold end diameter over which internal pressure can act is:

24 inch + 2 (1.5 inch) + 2 (1 inch) = 29 inch.

The peak axial working force on the manifold cover is:

(4.6 MPa) Pi [(29 inch / 2) X (.0254 m / inch)]^2

= 1.9602 X 10^6 Newtons

Consider use of 1.5 inch diameter flange bolts.

Bolt cross sectional area = Pi (0.75 inch)^2

= 1.767 inch^2

Assume that maximum permissible bolt load = 10,000 lb / inch^2

Note that this assumption implies use of high nickel alloy bolts to provide this bolt strength at 530 degrees C.

Then maximum load per bolt = 1.767 inch^2 X 10,000 lb / inch^2

= 17,670 lbs bolt

= 17,670 lbs X (9.8 kg m / s^2) / 2.2 lbs-bolt

= 78,712 Newtons / bolt

Hence the minimum number of perimeter bolts is:

1.9602 X 10^6 Newtons / (78,712 Newtons / bolt)

= 24.9 bolts ~ 25 bolts.

The bolt circle circumference is:

Pi (38 inch - 2 (2 inch) = Pi (34 inch)

= 106.81 inch

Thus the maximum perimeter bolt center to center spacing is about:

106.81 inch / 25 bolts = 4.2724 inch / bolt

For a stronger bolted assembly use 30 bolts spaced at:

106.81 inch / 30 bolts = 3.5603 inches / bolt

Consider use of 30 bolts with a stagger:

106.81 inch / 30 bolts = 3.56 inch / bolt.

In this case reduce one bolt circle to 33.5 inch and increase the other bolt circle to 34.5 inch. Then the bolt center to center distance becomes:

[(1 inch)^2 + (3.56 inch)^2]^0.5 = 3.698 inch.

Then the washer rim width must be less than:

(3.968 inch - 1.5 inch) / 2 = 1.234 inch

In summary the Intermediate Heat Exchange Bundle manifold has an ID of 24 inch and an OD of 38 inch. It is rated for a maximum working pressure of 4.6 MPa at 527 degrees C.

**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.

One seal method is to use soft metal gaskets. Such gaskets do not tolerate pipe misalignment or manifold distortion. Hence gasketed mechanical joints need close to optical precision fabrication. This precision is nearly 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.

The alternative sealing method is to machine optical flats and then edge weld all around. The weld is then mechanically stress relieved by the flange bolts. The disadvantage of edge welding is that the entire weld has to be removed with an edge grinder in order to obtain manifold interior access.

**INTERMEDIATE HEAT EXCHANGE BUNDLE TUBES:**

The intermediate heat exchange bundles have no shell so the diameter available for tubes is:

24 inches X 25.4 m / inch = 609.6 mm

Assume that the tubes are 0.7 inch center to center. Thus a 24 inch linear diameter will accept:

24 inch / 0.7 inch = 34.285 tubes.

Assume that the tubes are positioned on a square grid to allow adequate radial sodium flow. Then the theoretical maximum number of tubes is:

Pi (34 / 2)^2 = Pi (17)^2 tubes
= 907 tubes.

However, the outer perimeter ring contains:

Pi (34 tubes) = 107 tubes.

In order to allow for the perimeter weld between the tubesheet and the manifold side the outer tube ring will be lost leaving:

907 - 107 = **800 tubes / intermediate heat exchange bundle**

In half inch OD tubes the available wall thicknesses are:

.035 inch, .049 inch, .058 inch, .065 inch, .083 inch

Then for an intermediate heat exchange bundle the heat transfer rate across the tube walls is:

800 tubes X 2567.0 Wt / tube deg C _______= 2,053,600 Wt / deg C

Thus at a FNR thermal power of 900 MWt the temperature drop across the intermediate heat exchange tube metal is:

900 MWt / [(2.053600 MWt / deg C - bundle) X 56 bundles] = **7.826 deg C**

For the intermediate heat exchanger the end face cross sectional area is:

Pi (12 inch)^2

= Pi (144 inch^2)

For the intermediate heat exchanger the tubes reduce the inside shell cross sectional area by:

800 tubes X Pi (0.500 inch / 2)^2

= Pi (50.0 inch^2)

Thus for the intermediate heat exchanger the cross sectional area between the tubes is:

Pi (144 inch^2) - Pi (50 inch^2)

= Pi [94 inch^2]

= Pi [9.695 inch]^2

= Pi [19.391 inch / 2]^2

Hence the primary sodium flow into and away from the intermediate heat exchangers must be the equivalent in cross sectional area to a **20 inch nominal diameter pipe.**.

**MECHANICAL SUPPORT:**

The weight of the intermediate heat exchangers is primarily borne by a shelf inside the primary sodium pool. This shelf is supported by steel columns with bases that rest on the inside bottom of the primary sodium pool.

The intermediate heat exchange bundles are free to slide across this shelf to accommodate thermal expansion and contraction of the secondary sodium pipes and the primary sodium pool structure. The secondary sodium pipes must be long enough to accommodate the vertical flexing associated with thermal expansion/contraction of the shelf support columns.

**FLOW CONFIGURATION:**

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

Thus in the intermediate heat exchangers low pressure secondary liquid sodium flows inside the vertical heat exchange tubes. If there is a secondary sodium leak from the intermediate heat exchanger that secondary sodium will leak into the lower pressure primary sodium pool.

**INTERMEDIATE HEAT EXCHANGE BUNDLE CLEANING:**

Immediately underneath each intermediate heat exchanger is an intermediate heat exchanger sump. The purpose of this sump is to trap NaOH and other matter that is denser than liquid sodium. Periodically when the primary sodium is hot the secondary sodium induction pump is turned off and this sump is drained by a small diameter drain tube that runs from the bottom of the sump to an isolation valve and a catch basin. The pressure of the argon above the secondary sodium will drive the contents of the intermediate heat exchanger sump up the drain tube and into the catch basin, which is at ambient pressure.

**DISCONNECTION SAFETY:**

If an intermediate heat exchanger needs to be replaced the first step is to transfer all the contained secondary liquid sodium from this heat exchanger and its connected piping into the associated secondary sodium drian down tank. To expel secondary sodium from the intermediate heat exchanger tubes 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. Then the sodium contained in the intermediate heat exchanger sump is expelled into the sump catch basin. The remaining sodium in the intermediate heat exchanger is just that remaining in the sump drain tube.

In reality, even after this procedure is complete a small amount of secondary sodium will remain in the bottom of the intermediate heat exchanger sump. This small amount still 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 remove this remanent secondary sodium by vacuum suction. In general for safety the flanges connecting the intermediate heat exchanger and its radial piping should be closed with blanking plates while the intermediate heat exchanger is still in the reactor argon atmosphere.

**PRESSURE SAFETY:**

The secondary sodium pressure safety rupture disk must be able to discharge hydrogen gas from the secondary sodium circuit at a rate equal to the maximum rate of high pressure hydrogen formation. That rate is limited by the maximum water flow through the steam generator tube rupture(s) which is a function of the steam generator tube ID, the number of tubes ruptured and the differential pressure between the steam generator upper manifold and the secondary sodium.

In a practical accident scenario the water contacting sodium forms hydrogen which raises the secondary sodium pressure until the rate of hydrogen discharge equals the rate of hydrogen formation. Hence the secondary sodium rupture disk rating should be 4.6 MPa.

Each secondary sodium heat transport loop has expansion and dump tanks containing variable pressure argon. When the freeze valve isolating the dump tank is open the dump tank also acts as an expansion tank and attenuates any pressure pulses in the secondary liquid sodium.

**INTERMEDIATE HEAT EXCHANGER OPERATING CONDITIONS:**

At full load the intermediate sodium temperature differential is:

480 C - 330 C = 150 deg C

without threat of NaOH precipitation.

**INTERMEDIATE HEAT EXCHANGER CONSTRUCTION:**

The intermediate heat exchange tubes and manifolds must be strong enough to withstand the longitudinal force exerted by the peak secondary sodium pressure. In the event of an intermediate heat exchange tube wall failure intermediate sodium will flow through the tube rupture into the primary sodium pool. The preferred alloy for intermediate heat exchange manifold fabrication is 617 alloy. The intermediate heat exchanger mounting positions protect the intermediate heat exchange materials from neutron irradiation.

A significant issue is the overall length of the intermediate heat exchangers, including their sumps and their feed pipes. This overall length requires both sufficient overhead lifting clearance and sufficient air lock length.

Advanced Reactor Heat Exchangers reference file.The contemplated intermediate heat exchanger is realized using a 20 foot (6 m) lengths of (1 / 2) inch OD tubes. These tubes are available with sufficient wall thickness (0.065 inch)_______ to safely withstand the maximum sodium working pressure. The tubes terminate in 617 alloy tube sheets that form one side of the Intermediate Heat Exchange end manifolds.

Each 20 foot long intermediate heat exchange bundle will accept:
800 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:

800 tubes X 230 inches / tube X Pi X .435 inch_____ = 251,453 inch^2

= 162.227 m^2

The corresponding heat flow rate per steam generator bundle limited by Inconel 600 conductivity is:
20.9 Wt / m-deg K X 162.227 m^2 X (1 / .065 inch) X (1 inch / .0254 m) = 2,053,631 Wt / deg K

= 2.054 MWt / deg K

Thus temperature drop across the heat exchange bundle tube wall is:

(900 MWt / 56) / (2.054 MWt / deg K)

= 7.824 deg C

**INTERMEDIATE HEAT EXCHANGER MANIFOLD END CAPS:**

The intermediate heat exchange manifold end caps might have to be cast from Haynes 617 Alloy

**THERMAL SIPHON CALCULATIONS:**

Define:

V = linear sodium velocity in pipe

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:

800 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 HEREThe 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.

**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.

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.

**INTERMEDIATE HEAT EXCHANGE BUNDLE WEIGHT:**

Inlet Pipe = ____

Discharge Pipe = ____

2 X Flange = ______

2 X Tube Sheet= _______

Tubes =

Pi [(0.50 inch)^2 - (0.37 inch)^2][1 / 4] X (0.0254 m /inch)^2 X 6.1 m / tube X 800 tubes X (8000 kg_____ / m^3)

= 4621.36 kg

2 X Manifold = _______

Drain tube = _______

Lifting Point = _______

Hence the total intermediate heat exchange bundle weight will likely be about ______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.

**CONSTRUCTION:**

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 the primary sodium pool by lowering using the overhead gantry crane. Each unit rests on a shelf supported by a screw a jack for precise height adjustment. The height is adjusted for accurate alignment with the secondary sodium pipes to the heat exchange gallery.

**FNR INTERMEDIATE HEAT EXCHANGE TUBES:**

This web page deals with FNR intermediate heat exchanger tubes. A system design 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 330 degrees C to 520 degrees C.

It is shown that due to best performance under severe thermal stress the best heat exchange tube material for the intermediate heat exchangers is likely Inconel 600 or 617 alloy.

**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:

PROPERTY | 316L | HT-9 | D9 | 15/15Ti | INCONEL |
---|---|---|---|---|---|

Density | 7966 kg / m^3 | 8200 kg / m^3 | 8430 kg / m^3 | ||

TC @ 500 C | 15 W / m-K | 26.2 W / m-K | 20.2 W / m-K | 20.9 W / m-K | |

TCE @ 500 C | 18 X 10^-6 / K | 15 X 10^-6 / K | 13 X 10^-6 / K | 15.1 X 10^-6 / K | |

Y @ 25 C | 202 GPa | - | -- | 207 GPa | |

Y @ 250 C, no rad. | - | 2000 GPa | -- | -- | |

Y @ 250 C, with rad. | 2000 GPa | -- | -- | ||

Y @ 350 C, no rad | 860 GPa | ||||

Y @ 350 C, with rad | 1200 GPa | ||||

Bulk Y @ 500 C | 120 Gpa | 135 GPa | -- | ||

Sy @ 25 C, no rad. | 291.3 MPa | - | -- | 630 MPa | 550 MPa |

Sy @ 250 C, no rad. | 600 MPa | - | 570 MPa | - | |

Sy @ 250 C, rad | 900 MPa | - | - | ||

Sy @ 350 C, no rad. | 420 MPa | 560 MPa | - | ||

Sy @ 400 C, rad | 600 MPa to 900 MPa | - | - | ||

Sy @ 465 C, no rad | 725 MPa | - | 530 MPa | - | |

Sy @ 460 C, with rad | 520 MPa | - | - | ||

Sy @ 500 C, no rad | 167 MPa | 400 MPa to 550 MPa | 510 MPa | 579 MPa | |

Sy @ 500 C, with rad | 450 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.

<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:**

Look at 617.

**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

This web page last updated September 11, 2021

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