Home Energy Physics Nuclear Power Electricity Climate Change Lighting Control Contacts Links


XYLENE POWER LTD.

FNR INTERMEDIATE HEAT EXCHANGER

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

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

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

This web page deals with FNR intermediate heat exchanger and related heat transport and dimensional matters.

In the intermediate heat exchanger primary sodium flows down on the shell side and intermediate intermediate sodium flows up through the tubes.

The intermediate heat exchange bundles are single pass to realize a counter current heat exchanger.

In the steam generator intermediate sodium flows down through tubes and water/ steam flows up on the shell side.

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

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

PRIMARY SODIUM:
Other parties using liquid sodium for heat transport have experienced repeated sodium fires. A repeated problem is that when hot liquid sodium is inside a pipe at a pressure greater than atmospheric pressure the sodium tends to leak at any mechanical joint that is less than perfect. Frequently the liquid sodium operating temperature is too high for use of elastomeric gaskets. Once outside the pipe the sodium spontaneously ignites in air. That situation is unacceptable, especially if the sodium is radio active.

A solution to this problem used in this FNR design is to operate the primary sodium heat transfer circuit at a pressure less than ambient atmospheric pressure. This negative pressure is maintained by a siphon so that if a small leak occurs atmospheric gas leaks in rather than liquid sodium squirting out. Hence radioactive sodium is not expelled into the environment. This siphon pipe arrangement is enabled by the relatively low density of liquid sodium and by the design positioning of the intermediate heat exchangers.

To start the siphon a short term argon vacuum is applied. This vacuum line is routed more than 40 feet above the primary liquid sodium pool surface to ensure that liquid sodium is not sucked into the vacuum pump.

When atmospheric gas leaks into a siphon the siphon soon collapses and the contained radioactive sodium runs by gravity back to the primary sodium pool. Once the siphon collapses there is no primary sodium flow, so this leak is quickly detected, and the intermediate heat exchanger involved will soon cool to close to the steam generator makeup water temperature, which will enable safe service work on the intermediate heat exchanger after the intermediate heat transport fluid is transferred to its drain down tank. Then by adding a small positive argon pressure to the primary liquid sodium heat transfer pipe a bubble test can be used to locate the primary sodium pipe leak.

In reality, even after drain down a small pond of primary sodium might remain in the shell side of the intermediate heat exchanger. This small pond presents both a potential radio activity risk to maintenance personnel and a potential fire risk if at some later time oxygen is admitted into the primary sodium piping. The best way to minimize both of these risks is to have a small tube that connects onto the lower tube sheet and onto the discharge pipe such that this pond will spontaneously drain. However, a blockage in that tube might be difficult to detect other than by excessive radioactivity after drain down. Hence we will assume that the tube is blocked to evaluate the worst case radiation hazard.
 

EVALUATION OF POTENTIAL RADIATION HAZARD DUE TO TRAPPED PRIMARY SODIUM:
Volume of trapped primary sodium:
2 inch X Pi X (11 inch)^2 X (.0254 m / inch)^3 = 0.0125 m^3
Volume of primary sodium pool = 12 m X Pi X (10 m)^2 = 3770 m^3
Thus:
Volume of trapped primary sodium / Volume of primary sodium pool
= 0.0125 m^3 / 3770 m^3 = 3.315 X 10^-6

The number of reactor fissions / sec is given by:
[875 MWt / (200 MeV / fission)] X (1 J / Wt-s) X [1 / (1.602 X 10-19 J / eV)]
= 2.731 X 10^19 fissions / sec.

Assume that each fission results in 3 neutrons. Assume that 1% ______of the neutrons are absorbed by sodium. Then the rate of Na-24 atom formation is:
(2.731 X 10^19 fissions / s) X (3 neutrons / fission) X (0.01)
= 8.193 X 10^17 Na-24 atoms / sec

Then the maximum possible rate of Na-24 atom decay in the trapped sodium is:
8.193X 10^17 Na-24 atoms / sec X 3.315 X 10^-6 = 27.16 X 10^11 Na-24 atoms / sec

Assume that each of these decays results in emission of a 1.369 MeV gamma ray. Then the total gamma ray power emission by the trapped sodium is:
(27.16 X 10^11 Na-24 decays / s) X (1.369 MeV / Na-24 decay) X (1.602 X 10^-19 J / eV) X (10^6 eV / MeV)
= 59.57 X 10^-2 J / s
= 0.5957 J / s

This radiation is distributed over a spherical surface. At a distance of 1 m that area is 4 Pi M^2. However, a man working on fixing a leak in an intermediate heat exchanger might present a capture area of 1 m^2 and neglecting the absorption by the intermediate heat exchanger steel might absorb as much as (1 / 4 Pi) of this amount or about:
0.5957 J / (4 Pi s) = .0474 J / s

Assume that the worker's mass is 100 kg. Then his possible radiation exposure is:
(0.0474 J / s) / 100 kg = 4.74 X 10^-4 J / kg / s
= 4.74 X 10^-4 Gy / s

This is a potentiualloy dangerous dose rate and indicates the need for the aforementioned drain tube at the bottom of the intermediate heat exchanger.

Na-24 has a half life of 15 hours. If the equipment is allowed to cool down for a week then this exposure is reduced by a factor of 2000 to:
4.74 X 10^-4 Gy / s / 2000 = 2.37 X 10^-7 Gy / s

After 2 weeks this exposure is reduced to: = 0.427 X 10^-6 Sieverts / h
which is an acceptable occupational ionoizing radiation exposure level. Thus when work needs to be done inside a heat exchange gallery the primary sodium pipes feeding that gallery must be drained and then, if the radiation level does not immediately drop to a safe level indicating complete drainage of the primary sodium from the intermediate heat exchanger, the gallery must be left out of service for 10 days to two weeks to allow the gamma radiation level in that gallery to decay to a safe value. At that time the reason for incomplete drainage of primary sodium can be determined.
 

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

To meet these specifications for this FNR high pressure (11.5 MPa) non-radioactive sodium is used as the secondary heat transport fluid.

In the event of a tube rupture in the steam generator below the steam generator water level there is potential for a violent chemical reaction between the secondary sodium and water used as the turbine working fluid. If this chemical reaction took place in the secondary sodium circuit a hydrogen pressure pulse from this reaction might cause a liquid sodium hammer analogous to water hammer, possibly rupturing the intermediate heat exchanger and leading to major facility damage. Hence the intermediate heat exchanger must be designed to safely withstand large pressures and the secondary liquid sodium must always be at a higher pressure than the water in the steam generator to prevent water entering the secondary sodium circuit in the event of a steam generator tube rupture.

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

The secondary sodium in each heat transport loop can be transferred to and from the loop's drain down tank to permit service work on that pipe loop. This liquid sodium transfer is facilitated by a pipe connected between the bottom of the secondary sodium drain down tank and the lower manifold of the intermediate heat exchanger and by small argon injection/vent pipes connected to the top of the drain down tank and the highest point on the intermediate loop. Application of argon pressure over the drain down tank and relief of argon pressure from the top of the secondary sodium loop transfers liquid sodium into the secondary loop. Reversing this procedure allows secondary sodium to gravity flow back into the drain down tank. A liquid sodium detector should be provided at the top of the system to indicate when to close the top argon vent valve. The supply of argon for presurizing the drain down tank and the argon sink from the system top can both be from the pool enclosure. Similarly when drain down is required the argon in the drain down tank can be vented to the pool enclosure and after the argon pressure has sufficiently dropped the argon top vent valve can be openned. Note that for safty this argon top vent valve must be vented over the primary liquid sodium pool. Failure or premature openning of this vent valve could cause a high pressure high temperature stream of liquid sodium to be expelled.
 

FNR INTERMEDIATE HEAT EXCHANGER PRIMARY LOOP DESIGN CONCEPT:
The FNR intermediate heat exchanger takes advantage of the relatively low density and large thermal coefficient of expansion of liquid sodium.

In this equipment configuration the primary liquid sodium pool is 12 m deep. The concept is the feed primary liquid sodium to an external heat exchanger via a thermal siphon. The hot side of the thermal siphon draws lower density 490 deg C primary liquid sodium from about 3 m below the primary liquid sodium pool surface. The cool side of the thermal siphon discharges higher density 340 degree C liquid sodium to about 11 m below the primary sodium pool surface. Both the primary liquid sodium inlet and discharge sodium pipes to the intermediate heat exchanger are thermally well insulated.

Note that there is an upper limit on the primary liquid sodium inlet temperature to the intermediate heat exchanger of about 757 degrees C at which temperature the primary liquid sodium vapor pressure is 0.25 atmospheres. A sodium vapor pressure significantly higher than 0.25 atmosphere will prevent the thermal siphon operating as intended. Then there is only 0.75 bar available to support the sodium column above the top of the primary sodium pool. The thermal siphon relies on the difference pressure between the atmospheric pressure and the hot sodium vapor pressure to maintain the height of the sodium column from the primary sodium pool surface to the top of the intermediate heat exchanger tube bundle.

The shell side of the vertical intermediate heat exchanger contains radioactive primary liquid sodium. The absolute pressure in this liquid sodium varies from 0.25 atmosphere at the top to 1.0 atmosphere at the liquid sodium primary pool surface. The thermal siphon action is started using a vacuum pump connected to the highest point on the shell side of the heat exchanger to extract argon cover gas. The tube side of the heat exchanger contains non-radioactive intermediate sodium typically at a pressure of about 11.5 MPa. Note that the high pressure intermediate 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 on heat exchange tubes. The high temperature limit on the circulated intermediate sodium is 530 degrees C at low loads falling to about 490 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 causung NaOH precipitation. There is feed water recirculation through the bottom shell side of the steam generator to minimize thermal stress in the steam generator. The feed water temperature rise from 25 deg C to 320 C is realized by feed water recirculation and by recuperator heat recovery from the steam immediately upstream from the turbine condenser.

This arrangement also means that the pressure rating of the intermediate heat exchanger shell is only - 1 bar. However, the tubes and side wall must be strong enough to withstand the longitudinal force exerted by the high pressure intermediate sodium. In the event of an intermediate heat exchange tube wall failure the intermediate sodium will flow into the primary sodium pool.

Normally the intermediate sodium is used to heat an adjacent steam generator.

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

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.

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 fluid in the intermediate 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.

The reactor system consists of 56 independent identical heat transport systems so that a failure of one does not cause a failure of the whole.

Important sub-system components are the intermediate sodium reluctance pumps. These pumps must dependably operate at about 330 degrees C at a liquid sodium pressure of 11.5 MPa.
 

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____

Note that the water level in the steam generator is controlled which results in a steam generator liquid sodium discharge temperature of 321 to 330 degrees C.
 

ADVANTAGES OF THIS EQUIPMENT CONFIGURATION:
1) By allowing argon cover gas into the top of the intermediate heat exchanger primary circuit the contained radioactive sodium will entirely drain back to the primary sodium pool under gravity for fire suppression and for allowing service work around the intermediate heat exchanger without a reactor shutdown.

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

3) Reactor shutdowns for individual intermediate heat exchanger or steam generator maintenance or replacement are eliminated.

4) The airlock design for primary sodium pool access is simplified since the airlock need not accommodate intermediate heat exchange bundles.

5) The required volume of primary liquid sodium is reduced by about 15%.

6) There should be enough sodium natural circulation to dependably remove fission product decay heat so that the system remains safe on loss of electric power. However, there must be reliable backup power sufficient for re-starting the thermal siphons after a severe earthquake which might break the siphon action by causing primary sodium surface wave action sufficient to allow cover gas into the thermal siphons.
 

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

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

3) The primary sodium top surface temperature must never exceed 757 deg C or otherwise heat extraction from the primary sodium pool will stop due to thermal siphon flow failure.
 

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

Mass in sodium riser pipe = Rho A H
Change in mass due to thermal expansion
= [Rho A H][80 ppm / deg C X 150 deg C]
Siphon force = [Rho A H][80 ppm / deg C X 150 deg C][g]
Siphon power = [Rho A H][80 ppm / deg C X 150 deg C][g][V]
Kinetic Power = Rho (V^2 / 2) A V

Neglecting viscosity:
Siphon power = kinetic power
or
[Rho A H][80 ppm / deg C X 150 deg C][g][V]= Rho (V^2 / 2) A V
or
[H][80 ppm / deg C X 150 deg C][g]= (V^2 / 2)
or
V^2 = H [0.024][9.8 m / s^2]

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

The web page FNR HEAT EXCHANGE TUBES gives:
A = 56 Intermediate Heat Exchangers X Pi [17.515 inch / 2]^2 / Intermediate Heat Exchanger X [0.0254 m / inch]^2
= 8.705 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.

As shown on the web page titled: FNR HEAT EXCHANGE TUBES 18 inch diameter pipes are needed for forming the primary liquid sodium loops. These pipes will fit around the primary sodium pool perimeter.
 

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 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 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.
 

INTERMEDIATE HEAT EXCHANGER CONSTRUCTION:
The contemplated intermediate heat exchanger is realized using a 20 foot length of 24 inch diameter steel pipe. This pipe is available in sufficient wall thickness to safely withstand the steam pressure on the shell side of the steam generator.

Each 20 foot long X 2 foot outside diameter intermediate heat exchanger shell 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
 

Choose the Intermediate Heat Exchanger shell to be Schedule 40 pipe. OD = 610 mm Wall = 17.48 mm. Hence ID = 610 mm - 2 (17.48 mm) = 575 mm. The cross sectional open area outside the tubes is:
Pi [(575 mm / 2) X (1 inch / 25.4 mm)]^2 - 625 tubes (Pi)(0.25 inch)^2
= Pi [128.117 inch^2 - 39.06 inch^2)
= Pi [89.05] inch^2

This intermediate heat exchanger primary can be serviced by an 18 inch diameter pipe.

Note that the primary sodium flow is laminar.
 

END CAPS:
The heat exchanger end caps and the steam generator end caps may have to be cast from Haynes 617 Alloy
 

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. Threaded pipe hanger hardware provides fine adjustment of each heat exchange manifold feed pipe position to precisely align the 18.0 inch OD pipe connection sleeves. The 18 inch pipes should be spaced off the pool wall by about 0.8 m to allow for thermal expansion/contraction and earthquake movement.

The intermediate heat exchangers rest on dedicated columns. These columns carry the weight of the intermediate heat exchangers down to the concrete foundation.

Each intermediate heat exchanger has 18.0 inch OD, primary sodium inlet and discharge pipes that run horizontally through the adjacent wall. The primary inlet pipe connects to the shell side top and the primary discharge pipe connects to the shell side bottom. 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 Intermediate Heat Exchanger and Steam Generator pair 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 wll common to the primary sodium pool enclosure:
0.50 m space to inside surface of common wall with primary sodium pool
0.75 m intermediate heat exchanger maximum radius
4.00 m Center to center distance from intermediate heat exchanger 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 Intermediate Heat Exchanger and 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.
 

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

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

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 primary 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 so that these pipes remain in position when an intermediate heat exchanger is disconnected.
 

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

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

End cap = ________

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Hence total equivalent pipe length = 30 m

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

Required secondary sodium drain down tank volume = _______

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

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

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

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

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

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

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

This web page last updated June 9, 2020

Home Energy Physics Nuclear Power Electricity Climate Change Lighting Control Contacts Links