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XYLENE POWER LTD.

FNR INTERMEDIATE HEAT EXCHANGE BUNDLES

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

INTRODUCTION:
This web page deals with FNR intermediate heat exchange tube bundles and related heat transport matters.
 

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

To meet these specifications non-radioactive sodium is used as the secondary heat transport fluid.

In the event of an tube rupture in the steam generator below the 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 potentially 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.

The secondary liquid sodium in each heat transport loop is pressurized by an expansion tank containing variable pressure argon. This expansion tank also attenuates any pressure pulses in the secondary liquid sodium.

The liquid sodium in each heat transport loop can be transferred to and from a drain down tank to permit service work on that pipe loop. This transfer is facilitated by a small pipe connected to the lower manifold of each intermediate heat exchange bundle and by an argon injection/vent pipe connected to the top of the secondary loop expansion tank.
 

INTERMEDIATE HEAT EXCHANGE TUBE MATERIAL:
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. With natural circulation of the primary liquid sodium the liquid sodium at the bottom of the primary liquid sodium pool operates at about 340 degrees C and the liquid sodium at the top of the liquid sodium pool operates at about 440 degrees C. Various parts of a heat exchange tube normally operate in the temperature range 330 C to 440 C.

Another practical consideration in choosing the heat exchange tube material is its workability. Each FNR has 32 X 1648 = 52,736 intermediate 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, and transuranium actinides from 20 degrees C to 488 degrees C.
 

It is shown that due to good performance under severe thermal stress the best heat exchange tube material for the intermediate heat exchange bundles is likely Inconel 600. Note that the Inconel is not exposed to the reactor's neutron flux.
 

TUBE MATERIAL STRESS ISSUES:
A major issue in FNR design is combined pressure stress and thermal stress in the intermediate heat exchanger and the steam generator caused by high working pressures and potentially high differential temperatures across the heat exchange tube walls.
 

TEMPERATURE CONSTRAINT:
At low steam loads the intermediate sodium flow will decrease and the secondary id sodium discharge temperature from the FNR will rise to the highest primary liquid sodium temperature of about 450 degrees C. As the steam load increases the secondary sodium flow will increase and the secondary sodiuum discharge temperature will decrease to about 430 degrees C.

As the primary liquid sodium flows through the reactor at full power its temperature increases from 340 C to 440 C. In this temperature range in a fast neutron flux the fuel tube material HT-9 undergoes goes material embrittlement.
 

SECONDARY SODIUM HEAT TRANSPORT:
Define:
Fmi = secondary sodium mass flow.
Cpi = secondary sodium heat capacity = 1.26 kJ / kg-deg K for sodium
Delta Ti = change in intermediate sodium temperature = 100 deg K
Then for sodium:
Fmi Cpi (Delta Ti) = 1000 MWt
or
Fmi = [1000 MWt] / [Cps (Delta Ti)]
= {[1000 MWt]
/ [(1.26 kJ / Kg-deg K) (100 deg K)]} X {1 kJ / kWt-s} X {10^3 kWt / MWt}
= [(1000) / (1.26 X 100)] X 10^3 kg / s
= 7.94 tonnes / s
= (7.94 tonnes / s) / (0.927 tonnes / m^3
= 8.56 m^3 / s
= required intermediate volumetric sodium flow.

Since there are 32 intermediate heat exchange bundles, the required sodium mass flow rate in each bundle is: (8.56 X m^3 / s) / 32 Bundles = 0.267 m^3 / s-bundle
 

SECONDARY SODIUM PIPE PARAMETERS:
Each intermediate heat exchange bundle is served by 16 inch OD pipes. To withstand the high liquid sodium working pressure the chosen 16.0 inch OD pipe has:
ID = 12.812 inch
OD = 16.0 inch
Wall = 1.594 inch

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 = (0.267 m^3 / s) / [0.0831746 m^2)]
= 3.210 m / s

This intermediate liquid sodium flow will develop a momentum change pressure at a sharp 90 degree elbow of:
(3.210 m / s)^2 X 1 m^2 X 927 kg / m^3 = P X 1 m^2
or
P = (5.149 m / s)^2 X 927 kg / m
= 9552 kg / m s^2
= 9552 Pa
=0.0946 bar

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

INTERMEDIATE HEAT EXCHANGE TUBE MANIFOLDS:
The width of the individual heat exchange bundles is limited by the pressure withstand capabilities of the intermediate heat exchange bundle top and bottom manifolds. Assuming the two halves of each manifold are bolted together the strength of the flange bolts limits the manifold width. Standard flanging for nominal 16 inch pipe sets the manifold width at each connection pipe as 32.5 inches. The portion of the manifold that can accommodate tubes is a 12 inch wide central strip. For the FNR the strip is bent around in a J shape. In plan view the manifold length along the FNR radial direction is 2.2 m and the manifold width tangent to the FNR pool wall tapers from 1.8 m at the outer end of the manifolds near the pool wall to 1.4 m at the inner end of the manifolds at a radius of 7.7 m from the pool center. There is an allowance of 0.1 m between the manifold and the pool wall to accommodate pipe thermal expansion and contraction. Hence the radius of the sodium pool at the inner end of the manifolds is:
10 m - 0.1 m - 2.2 m = 7.7 m
The circumference of a circle radius 7.7 m is:
Pi (2)(7.7 m) = 48.38 m.

When all 32 intermediate heat exchange bundles in place at a radius of 7.7 m they occupy: 32 X 1.4 m = 44.8 m of circumference. Hence they will fit with a gap of:
48.38 m - 44.8 m = 3.58 m which is sufficient for providing reactor access for intermediate heat exchange bundle replacement or for fuel bundle replacement.

At a radius of 9.5 m from the pool center the circle circumference is: Pi (2) (9.5 m) = 59.69 m

Standard flanging for 64 X 16 inch pipes requires:
64 X 32.5 inch X 0.0254 m / inch = 52.83 m

There is a gap of up to:
59.69 m - 52.83 m = 6.86 m
which is adequate allowance for pool access with all the intermediate heat exchange bundles in place.
 

INTERMEDIATE HEAT EXCHANGE TUBE CONFIGURATION:
Assume that the intermediate heat exchange tubes are located on 0.75 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. Hence a 12 inch width for tubes allows:
(12 inch / row) / (0.75 inch / tube) = 16 tubes / row.

The available strip length that can be occupied by tubes is at least 77.6 inches.

Then the maximum possible number of tube rows per intermediate heat exchange bundle is:
77.6 inch / 0.75 inch / row = 103.46 rows or 103 rows.

Then the number of tubes per intermediate heat exchange bundle is:

16 tubes / row X 103 rows = 1648 tubes / intermediate heat exchange bundle.
 

INTERMEDIATE HEAT EXCHANGE BUNDLE MOUNTING:
The intermediate heat exchange bundles are mounted along the primary liquid sodium pool walls. Each heat exchange bundle has 16.0 inch OD, 12.812 inch ID inlet and discharge pipes that run directly above the bundle. The inlet pipe is lower and the discharge pipe is higher. This configuration provides heat exchange counterflow and permits removal and replacement of individual heat exchange bundles together with their service pipes. The heat exchange bundles are connected single pass.

There are 16.0 inch OD 12.812 inch ID pipes from each port of each heat exchange bundle manifold up to 90 degree elbows and then back towards the steam generators. Each 16.0 inch OD inlet pipe to a heat exchange manifold has an induction type circulation pump and a disconnection flange. Each 16.0 inch heat exchange manifold discharge pipe has a disconnection flange.

The heat exchange bundles are completely isolated from one another. Each bundle feeds a dedicated steam generator and has a dedicated expansion tank. Hence in the event of a problem one heat transport loop can be shut down while the other heat transport loops remain fully operational.

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

The hot secondary liquid sodium is piped outside the reactor building to adjacent buildings that contain steam generators and associated downstream non-nuclear equipment. Under ordinary operation the reactor power is modulated by controlling the intermediate sodium circulation rate. The intermediate sodium heat transport pipes must have at least two 90 degree elbows with arms sized to allow for thermal expansion-contraction and possible earthquake related movement.
 

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 1648 tubes / bundle
= 0.1143 m^2
 

INTERMEDIATE SODIUM CIRCULATION PUMP:
The open cross sectional area of the intermediate heat exchanger secondary is much larger than the external pipe cross sectional area which means that the secondary sodium circulation pump must be sized to create the kinetic flow power in the secondary external piping. Since the same issue pertains to the steam generator the intermediate liquid sodium circ pump must be sized to create more than twice the kinetic flow power in the external piping. Note that this pump should be located on the low temperature return pipe and should be physically near the bottom of the secondary pipe loop to ensure positive suction head.
 

INTERMEDIATE SODIUM PUMPING POWER:
The intermediate liquid sodium acceleration power associated with each straight pipe section is:
[(mass flow rate) / 2] X (flow velocity)^2
(mass / volume)(area)(flow velocity /2)(flow velocity)^2
= (927 kg / m^3)(0.08317 m^2) (3.210 m / s)^3 (.5)
= 1275 kg m^2 / s^3
~ 1.275 kW

There are at least two such accelerations in a typical secondary sodium circuit and the pumps are unlikely to be more than 20% efficient.

Each loop needs at least 2.55 kW 0f mechanical circulating energy. If the induction pump is 20% efficient each intermediate loop needs:
5 X 2.55 = 12.75 kWe
of pumping electric power. Hence the total intermediate sodium pumping electricity requirement is at least:
32 X 12.75 kW = 408 kWe___________________

Allowing for flow pressure drops across the intermediate heat exchangers and the steam generators the total liquid sodium secondary pumping power will likely be of the order of one MWe.
 

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. Hence the intermediate heat exchanger, its secondary sodium pump and its related steam generator need precision fabrication and alignment.
 

SECONDARY LIQUID SODIUM FLOW:
There are 32 intermediate heat exchange bundles. The heat exchange circuits are completely isolated from one another. Each intermediate heat exchange bundle feeds a dedicated steam generator. Hence in the event of a heat exchange tube problem any heat transport system can be shut down while keeping the other heat transport systems fully operational.

There are 16.0 inch OD, 12.8122 inch ID pipes from each end of each heat exchange bundle manifold up to 90 degree elbows and then back towards argon tight wall penetrations. All the heat exchange bundle manifolds and the liquid sodium pipe and fitting disconnection flanges are sealed with soft metal gaskets.

The hot secondary liquid sodium rises and then passes through the adjacent concrete wall enroute to a nearby steam generator. Under ordinary operation the reactor power is controlled by modulating the secondary sodium flow rate.

The immersed heat exchange bundles are realized with vertical tube bundles. To minimize longitudinal thermal stress on the tubes the lower tube manifolds are unsupported except by the tubes and external pipes. The upper tube manifolds are positioned near the liquid sodium surface level and are supported by the 16.0 inch OD pipes. Threaded pipe support hardware provides fine adjustment of each heat exchange maniflold position to precisely align the 16.0 inch OD pipe disconnection flanges. These flanges have an OD of about 32 inches.

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 immersed heat exchange bundles are single pass with one bypass tube connected to the lower manifold to permit easy expulsion of liquid sodium from this loop using compressed argon. The upper manifold has a main chamber and a small vent chamber. The vent chamber has a small vent valve.

The intermediate heat exchange tube bundles are baffled on the primary sodium side to realize a counter flow heat exchange configuration with a smooth temperature transition. Primary liquid sodium flows over the baffle top, down between the tubes and out under the baffle bottom. Each heat exchange bundle manifold is piped to a dedicated steam generator with the secondary circulation pump on the lower cool side of the loop. This arrangement minimizes the requirement for valves. The liquid sodium injection/removal port has a low temperature valve.

This configuration balances flows, optimizes heat transfer and minimizes thermal stresses. The standard manifold piping connection arrangement for each heat exchange bundle has one 16 inch circulation pump, one 16 inch OD pipe wall penetration, one 16 inch horizontal straight pipe section, one 16 inch OD 90 degree elbow, one 16 inch OD vertical pipe section, the heat exchange bundle lower manifold, the heat exchange bundle tubes, the heat exchange bundle upper manifold, one vertical 16 inch pipe section, one 16 inch 90 degree elbow, one 16 inch horizontal straight pipe section, one more 16 inch wall penetration, one argon cushion tank, the steam generator inlet, the steam generator tubes and a 16 inch straight pipe section back to the circulation pump. There is one small drain valve on each heat exchange bundle. This arrangement permits practical and safe identification, isolation, draining, replacement and refilling of any defective heat transport loop component.The heat exchange bundles must have sufficient positioning play to allow for pipe thermal expansion-contraction and possible earthquake related movement.
 

INTERMEDIATE HEAT EXCHANGE BUNDLE SIZING:
The heat exchange bundle sizing is largely determined by the required thermal power and discharge temperature, the thermal conductivity characteristics of the heat exchange bundle tubes and the temperature profile of the primary liquid sodium.

One of the principal constraints on heat transfer is the wall thickness of the heat exchange bundle tubes. The heat exchange tubes in the intermediate heat exchanger are chosen to be .500 inch OD tubes with .065 inch wall spaced on a square grid with 0.75 inch square centers.

Hence the ID of this heat exchange tube is:
0.500 inch - 2(.065 inch) = 0.370 inch

The long term yield stress of Inconel 600 at less than 600 deg. C is about 579 MPa. Ontario pressure vessel safety codes require a safety factor of 3. Hence the maximum material working stress at 600 deg. C should be (579 MPa / 3) = 193 MPa. The combined tube wall thickness is:
2 X .065 inch = 0.13 inch.
The tube inside diameter is:
(0.500 inch - .13 inch) = .370 inch

Application of Barlow's formula gives the maximum allowable internal working pressure with no thermal stress as:
193 MPa X (.13 / .370) = 67.81 MPa. This pressure is divided by two again to allow for thermal stress, so the maximum rated working pressure is 33.90 MPa. However, the normal working pressure of the steam system is less than 12 MPa. Thus the heat exchange tubes in the intermediate sodium loop have a large pressure/stress safety margin.

The condensate feed pump control system should be designed such that the maximum design system operating pressure of 11.2 MPa is never exceeded.

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

SECONDARY SODIUM PRESSURE CHANGE DUE TO NATURAL CIRCULATION:
In normal full load reactor operation the reactor produces 1000 MWt of heat. When the chain reaction is off the reactor may still produce as much as:
1000 Mwt / 10 = 100 MWt
of fission product decay heat.

Hence natural circulation of the secondary sodium should run at 5% to 10% of the pumped circulation rate. Note that if there is too much natural circulation the induction pumps should be operated to retard the natural 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 1648 tubes / bundle the secondary sodium natural circulation flow rate per bundle is:
1648 tubes/bundle X 6.23515 X 10^-5 m^3 / s-tube = 0.10275 m^3 / s-bundle which is several times the minimum required natural circulation rate.

In order to have a full range of FNR modulation it will be necessary to have induction pumps that can pump backwards in order to reach a minimum steam output condition for each steam generator.
 

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 failure and chain reaction shutdown but continued reactor heat production due to fission product decay.
 

CONDENSATE INJECTION:
A key issue on loss of control power is to maintain condensate injection into the steam generators. On loss of control power the steam generator pressure control valves must open to reduce the pressure in the steam generators so that condensate injection into the steam generators can occur via a gravity water feed. Hence the cooling tower condensate collection tank must be at a higher elevation than the steam generators and the injection pumps must be shunted by non-return valves to permit gravity fed injection to occur when the injection pumps are off.
 

INDIVIDUAL HEAT EXCHANGE BUNDLES:
As shown above each intermediate heat exchange bundle has 1648 tubes / bundle. Assume use of 0.500 inch OD inconel tubes with .065 inch wall thickness. The total active intermediate heat exchange tube length is: 32 bundles X 1648 tubes / bundle X (6.0 m) / tube = 316,416 m

This parameter compares with a reactor active heat exchange tube length of:
(476 tubes / active fuel bundle) X (640 active fuel bundles) X (0.35 m / tube) = 106,624 m,
suggesting that the temperature drop across the intermediate heat exchanger tube wall is about:
(1 / 3) 15 dg C = 5 deg C.

An important issue is the relative thermal conductivities of Inconel 600 and steel.

The thermal conductivity of Inconel 600 is assumed to be:
20 W / m-deg C

Hence the full load temperature drop across the intermediate heat exchange tube wall should be ~ 15 deg C / 3 = 5 deg C.

However, there is a problem that 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:
1000 X 10^6 Wt / 32 bundles = (delta T) (70.53 Wt / m-deg K) X 1648 tubes X 6 m X Pi X (0.5 inch) / (1 / 8) inch
or
(delta T) = 10^9 Wt / {(32 bundles) X (70.53 Wt / m-deg K) X (1648 tubes / bundle) X 6 m X Pi X (0.5 inch) / (1 inch / 8)}
= 3.565 deg K

Hence the total temperature drop across the intermediate heat exchange bundles at full power is about:
3.565 deg C + ~ 5 deg C = 9 deg C.

AN ISSUE THAT REMAINS TO BE CHECKED IS THE PRIMARY SODIUM FLOW RATE THROUGH THE INTERMEDIATE HEAT EXCHANGER. The open area is about:
1648 tubes X [(0.75 inch)^2 - Pi(1 inch / 4)^2] / tube X (.0254 m / inch)^2
= `1648 [0.5625 - 0.1963] X (.0254 m)^2
= 0.3893 m^2

The corresponding open area for the rising secondary sodium is:
1648 tubes X [Pi (0.37 inch / 2)^2] / tube X (.0254 m / inch)^2
= 0.1143 m^2

A key issue is whether the intended 100 degree C temperature drop is enough to drive the primary sodium to circulate at a rate which is about 0.29 X the secondary pumped sodium flow rate?

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 an orifice to the primary side of the intermediate heat exchanger baffle. We need to maintain the design temperature differential across the reactor in order to develop the required primary sodium natural circulation through the reactor.

Note that the intermediate heat exchange tube bundle is surrounded by an insulating baffle with inside dimensions of 16 inches X 77.3 inches. This baffle is open at its top and bottom to admit and discharge liquid sodium. The baffle port detail may have to be experimentally determined.

Each intermediate heat exchanger handles up to 31.25 MWt of heat which in turn can provide up to 10 MWe of turboelectricity generation. Thus the total reactor electricity output is limited by the heat transport system to:
32 X 10 MWe = 320 MWe
 

INTERMEDIATE SODIUM VOLUME:
The volume of each intermediate 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 12.8 inch inside diameter pipe.

Thus the minimum pipe length equivalents are:
Intermediate heat exchanger = 12 m
Steam generator = 12 m
Horizontal pipes = 2 X (4 m + 8 m + 4 m) = 32 m
Vertical pipes = 2 X 15 m = 30 m

Hence total equivalent pipe length = 86 m

Pipe volume = Pi (6.4 inch)^2 X 86 m X (.0254 m / inch)^2 = 8.135 m^3_______

Thus the total secondary sodium volume is about:
32 X 8.135 m^3 = 260 m^3
 

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

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

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

FOR 316L STAINLESS STEEL HEAT EXCHANGE TUBES:
(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 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.

The intermediate heat exchange tube area is:
Pi X (.500 inch) X (.0254 m / inch) X 6.0 m / tube X 32 bundles X 924 tubes / bundle = 7078.25 m^2

For Inconel 600 tubes the heat transport capacity is:
10 deg C X 7078.25 m^2 X 20 W / m-deg C X (1 / .065 inch) X (1 inch / .0254 m)
= 891749118 Wt
= 891.749 MWt

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

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}
 

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.

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

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.
 

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:
The absolute maximum temperature drop across an Inconel tube wall is:
(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 gas pressure further reduce the operating temperature differential by another factor of two to 61.75 degrees C.

Thus the conservative maximum operating heat flux through the Inconel 600 tubes of the intermediate 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 (.37 inch) X (.0254 m / inch) X 6.0 m / tube X 924 tubes / bundle X 32 bundles = 5237.91 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
= 9.8 MPa when the thermal stress is high.  

This web page last updated March 30, 2018

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