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

A nuclear reactor produces heat. The most practical way to convert that heat into electricity is by using the heat to produce high pressure steam. The steam expands while turning a steam turbine which in turn directly drives a line synchronous generator which produces 60 Hz 3 Phase electric power.

In a liquid sodium cooled Fast Neutron Reactor (FNR) for safety purposed there are isolate intermediate liquid sodium heat transport loops between the primary sodium in the reactor and the steam generator. This web page is concerned with the detail of the steam generator.

A FNR's steam generator differs from the steam generator of a water cooled nuclear reactor because the temperature differential of a FNR's intermediate heat transport loop is much higher than the temperature differential used in the heat transport loop of a water moderated reactor. The heat capacity of sodium is much less than the heat capacity of water. To make up for that difference in heat capacity the temperature differential across a FNR liquid sodium heat transport loop is much higher than the temperature differential for a similar thermal power transport capacity water loop. However, high temperature differentials lead to high thermal stress in the steam generator tube walls which are immersed in liquid water unless this thermal stress is reduced by changing the intermediate liquid sodium temperature profile. The temperature profile is changed by appropriate recirculation of liquid sodium drawn from the steam generator discharge.

A steam generator contains liquid water in its lower portion and steam in its upper portion. In a FNR steam generator there are four lower tube bundles fully immersed in liquid water and there is one upper tube bundle located in the water vapor above the water. A pressure regulating steam discharge valve keeps the pressure inside the steam generator at 11.5 MPa. This vapor pressure in combination with the properties of water keeps the liquid water at 320 degrees C.

The upper bundle raises the steam disscharge temperature to about 390 degrees C at full load. At light loads this steam discharge temperature rises to about 420 degrees C.

The heat exchange tubes of the upper tube bundle have their radial heat flux limited by the boundary layer at the metal tube-water vapor interface. In this upper tube bundle the temperature of the heat exchange tube metal is close to the temperature of the contained liquid sodium (410 C to 430 C), so the thermal stress within the tube metal is small.

The heat exchange tubes of the lower tube bundle, which is fully immersed in water, have liquid sodium inside the tube and liquid water outside the tube. Hence the temperature difference between the two liquids is dropped across the metal tube wall. To minimize thermal stress it is essential to keep this temperature difference within the tube material rating. A practical way of accomplishing this objective is to recirculate liquid sodium from the lower tube bundle sodium discharge back to the upper tube bundle discharge. There must be sufficient pipe length between this pipe junction and the lower tube bundle inlet to ensure good liquid sodium thermal mixing. This recirculation requires additional electric induction pumps with a combined flow of about 3X the intermediate heat transport loop flow.

At full thermal load the resulting temperature distribution is as follows:
Steam generator water temperature = 320 C
Steam generator steam discharge temperature = 390 C
Upper tube bundle sodium inlet temperature = 430 C
Upper tube bundle sodium discharge temperature = 410 C
Lower tube bundle sodium inlet temperature = 350 C
Lower tube bundle sodium discharge temperature = 330 C
Intermediate heat transport loop flow rate = Fi
Recirculation sodium flow rate = Fr
Lower bundle sodium flow rate = (Fi + Fr)

At the inlet to the lower bundle:
Fr (330 C) + Fi (410 C) = (Fi + Fr) 350 C
Fi(410 C - 350 C) = Fr (350 C - 330 c)
(Fr / Fi) = 3

We should control the intermediate loop pump and the steam generator recirculation pumps to all track each other. Then the steam generator steam discharge temperature will be a constant ~ 390 C and the steam flow will be proportional to the intermediate loop pump rate.

At low thermal loads the intermediate loop liquid sodium flow rate will be low. The recirculating sodium will be at a temperature close to 320 C and kept there by the pressure - temperature relationship maintained by the steam generator steam discharge valve.

At high thermal loads the intermediate loop sodium flow rate is much higher. The recirculating sodium temperature rises about 10 degrees C to deliver more heat to the water filled portion of the steam generator. However, the temperature difference across the lower bundles is never more than 25 C. Practical construction of this steam generator requires two portions, one on top of the other. The lower tube bundles are fully immersed in water and heat that water to about 320 C and also provide the latent heat of vaporization. In the upper part of the steam generator there is no liquid water and steam is further heated to about 390 C.

The recirculation pump flow rate is 3X the intermediate loop flow rate. Hence the liquid sodium flow rate through the lower heat exchange bundles is 4X the liquid sodium flow rate through the upper heat exchange bundle. Hence the cross sectional area of the tubes in the lower heat exchange bundles should be about 4X the cross sectional area of the tubes in the upper heat exchange bundle. In effect there are 4 fully immersed lower tube bundles in parallel and one upper tube bundle in vapor.

The lower tube bundle must raise the water temperature from the condenser recuperator discharge temperature to 320 C and must supply the latent heat of vaporization of water at the steam generator operating pressure. The upper tube bundle must supply the sensible heat required to raise the steam temperature from 320 C to the steam generator discharge temperature of about 390 C to 410 C. The upper tube bundle may also have to supply heat to vaporize small liquid water droplets that the flowing steam carries with it. It is important to vaporize these water droplets to prevent them eroding the down stream steam turbine.

With the aforementioned arrangement the maximum temperature difference across a tube bundle metal wall is about 30 degrees C. The cost of the electric induction pumps required for steam generator liquid sodium recirculation is a non-trivial issue.

Assume each intermediate heat exchanger bundle feeds one tall steam generator.

The steam generator must withstand the steam pressure. However, the steam generator has turbulent fluid flow on both sides of its tubes so it can operate with less tube area than the corresponding intermediate heat exchange bundle.

The contemplated steam generator is realized using 1.5 20 foot lengths of 36 inch diameter thick wall pipe welded together. 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 3 foot inside diameter steam generator shell will accept: (Pi) {[(18)^2 - (8)^2] / (.75)^2} ~ 1452 tubes. Within each such steam generator bundle there is a heat exchange area of:
1452 tubes X 220 inches / tube X Pi X .37 inch = 371,313 inch^2
= 240 m^2

The corresponding heat flow rate per bundle limited by Inconel 600 conductivity is: 20.9 Wt / m-deg K X 240 m^2 X (1 / .065 inch) X (1 inch / .0254 m) = 3,038,158 Wt / deg K
= 3.038 MWt / deg K

Thus with a 10.5 degree K drop across the heat exchange bundle tube wall the conducted thermal power transfer is:
3.038 MW / deg K X 10.5 K = 31.899 MWt

On this basis the total reactor heat exchange capacity with a 10 degree K temperature drop is:
32 heat exchange bundles X 31.899 MW / bundle = 1020.7 MWt

This web page last updated January 15, 2019

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