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

This web page deals with FNR intermediate heat exchange tube bundles.

The FNR requires a heat exchanger secondary fluid that is compatible with the heat exchange bundle material (Inconel 600) and will not chemically react with the hot radioactive liquid sodium in the event of a heat exchange bundle failure. This 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 heat exchanger secondary fluid.

In the event of an internal failure in the steam generator there is potential for a violent chemical reaction between the heat exchange 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 leading to major facility damage. Hence the intermediate heat exchanger must be designed to safely withstand large pressures and the secondary liquid sodium should always be at a higher pressure than the water in the steam generator to prevent water entering the secondary sodium circuit.

The intermediate heat exchanger secondary fluid is pressurized by expansion tanks containing variable pressure argon. These expansion tanks will also assist by attenuating any pressure pulses in the liquid sodium.

One of the best heat exchange tube materials for use in the intermediate heat exchanger and steam generator is Inconel 600.

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 tube walls.

At low steam loads the intermediate sodium flow will decrease and the intermediate sodium discharge temperature will rise to the highest primary liquid sodium temperature. As the steam load increases the intermediate sodium flow will increase and the intermediate sodiuum discharge temperature will decrease.

As the 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 HT-9 undergoes goes material embrittlement.

Fmi = intermediate sodium mass flow.
Cpi = intermediate 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
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

The flow cross sectional area of each 16.0 inch OD, 12.812 inch ID 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. Then:
V = (0.267 m^3 / s) / [0.0831746 m^2)]
= 3.210 m / s
in the 16 inch OD pipe.

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
P = (5.149 m / s)^2 X 927 kg / m
= 9552 kg / m s^2
= 9552 Pa
=0.0946 bar

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 1632 tubes / bundle
= 0.1132 m^2

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.

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.

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

There are 32 heat exchange bundles, 16 at each end of the primary liquid sodium pool. 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 fitted with soft metal gaskets.

The hot secondary liquid sodium is passes through the adjacent concrete wall to a nearby steam generator. Under ordinary operation the reactor power is set by adjusting 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 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 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 along 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.

The intermediate heat exchange bundles are in two rows adjacent to the primary liquid sodium pool end 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 closer to the pool end and the discharge pipe is higher and closer to the pool middle. 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, with the inlet port closer to the pool end and the discharge port closer to the pool centre.

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.

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 heat exchanger manifold width. Standard flanging for nominal 16 inch pipe sets the manifold width as 32.5 inches. The portion of the manifold that can accommodate tubes is the 12 inch wide central strip.

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 should be pressure limited to:
48.0 MPa / 3 = 16.0 MPa
which is the maximum intermediate sodium working pressure for the intermediate sodium piping.

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

Assume that each heat exchange bundle is intermediate liquid sodium connected to a steam generator using 16.0 inch OD, 12.812 inch ID steel pipe. Assume use of 0.500 inch OD inconel tubes with .065 inch wall thickness. Then neglecting viscosity considerations for cross sectional area matching each heat exchange bundle should have:
(12.812 inch / 0.37 inch)^2 = 1199 tubes / bundle.

However, the above calculation does not take into consideration either viscosity or thermal loading.

In the above calculation the total active intermediate heat exchange tube length is: 32 bundles X 1199 tubes / bundle X (6.1 m) / tube = 234,045 m

This parameter compares with a reactor active heat exchange tube length of:
532 tubes per active fuel bundle X 532 active fuel bundles X 0.35 m / core rod = 99,058 m

A key 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

We need to increase the number of intermediate heat exchange tubes to reduce the intermediate heat exchange tube wall temperature drop and to reduce the secondary liquid sodium flow resistance.

Assume that the heat exchange tubes are located on 0.75 inch rectangular grid to allow external primary liquid sodium to easily penetrate the tube bundle. Hence a 12 inch width for tubes allows:
(12 inch / row) / (0.75 inch / tube) = 16 tubes / row.

The available length that can be occupied by tubes is: 3.0 m - 32.5 inch - 8 inch = 3.0 m - (1.029 m)
= 1.97 m
= 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.

The required minimum length of this heat exchange bundle, including one 16 inch pipe end support and a manifold divider is:
77.6 inch + (32.5) inch + (8) inch = 118.1 inch
= 2.999 m

For ease of assembly and maintenance allow 6.5 inchs of clearance space between adjacent heat exchange bundles. Then each heat exchange bundle occupies 39 inches (1 m) of pool width. The maximum possible number of heat exchange bundles at each end of the pool is:
18.4 m / (39 inch X .0254 m / inch) = 18.57
We eliminate 2 bundles from each pool end to allow for service access leaving 16 intermediate heat exchange bundles per pool end.

Each intermediate heat exchanger handles about 30 MWt of heat. The corresponding steam generator steam outputs can be manifolded together in pairs to provide 60 MWt of steam which in turn provides 20 MWe of turboelectricity generation. Thus the total reactor electricity output is limited to:
16 X 20 MWe = 320 MWe

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 = 16 m
Steam generator = 18 m
Horizontal pipes = 2 X (4 m + 8 m + 2 m) = 28 m
Vertical pipes = 2 X 3 m = 6 m

Hence total equivalent pipe length = 68 m

Pipe volume = Pi (6.4 inch)^2 X 68 m X (.0254 m / inch)^2 = 5.645 m^3

Thus the total secondary sodium volume is about:
32 X 5.645 m^3 = 180.65 m^3

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:
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--

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 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 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, transuranium actinides from 20 degrees C to 488 degrees C.

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

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.

= (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 6.1 m / tube X 32 bundles X 1648 tubes / bundle = 12,834.8 m^2

For Inconel 600 tubes the heat transport capacity is:
10 deg C X 12,834.8 m^2 X 20 W / m-deg C X (1 / .065 inch) X (1 inch / .0254 m)
= 1554791036 Wt
= 1554.7 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 across the intermediate heat exchange tube walls is given by:
P (.37 inch) = (Syp / 6) 2 (.065 inch)
P = (Syp / 6)(0.13 inch / 0.37 inch)
= 30,000 psi (.05855)
= 1756.7 psi
= 119.5 bar
= 12.07 MPa

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}
+ {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.

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.

There are 16.0 inch OD 12.812 inch ID pipes from each end 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 point in the pipe mains are sealed sodium sumps with sufficient volume to accommodate all the liquid sodium in the relevant intermediate heat transport circuit. Sodium is transferred from this sump to the intermediate heat transport circuit by applying argon pressure over the sump while evacuating the loop cushion tank. These sumps require electric immersion heaters for liquid sodium melting/temperature maintenance. Note that these sumps must be rated as pressure vessels and must ve fitted with high pressure valves and 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 transport pipes must have at least two 90 degree elbows with arms sized to allow for thermal expansion-contraction and possible earthquake related movement.

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 0.75 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.

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.

(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 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 1500 tubes / bundle X 36 bundles = 11,844 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
Maximum pressure = 4067 psi X .130 inch / .37 inch
= 1429 psi
= 97.2 bar

This web page last updated September 3, 2017

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