Stirling engine correspondence

3 November 2011

Lars Harald Heggen's complete responses to two queries about his proposal to use a Stirling engine to remove decay heat from a nuclear reactor in a situation of station blackout

1. RESPONSE to MHI query about the necessary size of a Stirling engine to provide emergency cooling of a nuclear reactor

I will try to outline some general assessment of Stirling engines. I assume an engine that requires 100 kW of heat to run.

Engines available on today market operate on high temperature differences and are compatible with diesel or petrol engines in size. For example, Kockums and Stirling Biopower are two suppliers.

I think, the Japanese Navy is familiar with Kockums engines:

The second engine is a 25kW Generator set made by Stirling Biopower:

The engines of this type use either hydrogen or a noble gas (normally Helium) as the working media. The efficiency of these engines is typically 25% to 30%, meaning that for 100 kW of heat (that is transferred from the hot to the cold side) one gets 25kW to 30kW of mechanical power output.

Stirling engines, as powered by a reactor, would normally be operating on a “low” temperature difference. For the working media in such engines a noble gas will probably be the best choice. Helium and Argon are suitable working media, and the reason why most Stirling engines run on noble gases is that these gases give the best efficiency of the engine. This can be seen by dividing rate of expansion on rate of energy applied. Or R : c – individual gas constant : specific heat capacity. As mentioned earlier, for a 25 kW engine one would need 100 kW of heat to be transported from the hot to the cold side.

For this calculations I will make 4 assumptions:

1) The gas in the Stirling engine is at normal atmospheric pressure, 1 bar. (Normally the working media is pressurized, but it would probably be difficult to pressurize it more than to 2 or 3 bars, because of the size of this engine. The mechanical design of the engine would be difficult.)

2) The temperature difference for the engine I set to be 200 Kelvin. (250°C on the hot side, 50°C on the cold.)

3) The engine speed I set to 60 rpm = 1 Hz. (This is to simplify the calculations in the attached spread sheet. 1kW = 1kJ / 1 sec )

4) Using Boyle’s law, and assuming an Isobar expansion for the engine instead of an Isoterm, we get an idea of the amount of working media and the size of such an engine. (This last assumption is not correct, but is done to simplify the calculations.)

See attached spreadsheet where I list several possible gases as working media.

And if we look at Helium:

For a 25 kW engine (that is an engine that moves approximately 100 kW of heat from the hot to the cold side), the mass required to be moved from the hot to the cold side with every revolutions is 0.096 kg of He.

The volume of He at 50°C is 0.642m3. The heat exchanger for such engine would, as an assessment, be between 5 to 10 times this size. That means between 3.21m^3 to 6.42m^3.

The cylinder would need 0.397m^3 (1.039m-0.642m^3) of expansion volume if Isobar expansion is assumed.

With the four assumptions above and these figures we can assume such engine to be some 4m^3 to 7m^3 in size.

BUT, if we alter the assumptions to be a pressurized engine with a 2 bar pressure of the working media, and the speed of the engine to be 120 rpm (2 Hz), we can divide the size by 4 (2 x 2), and the engine size will be some 1m^3 to 2m^3.

2. RESPONSE to Westinghouse query about the delay in startup time required for a Stirling engine to provide emergency cooling of a nuclear reactor

If a reactor has other emergency cooling systems (as for example GE’s 6 days + system, presented at the WNA symposium), then both systems would complement one another. But if we just regard a Stirling engine, the following startup system can be added in order to adjust it to meet the requirements of a specific startup time.

First I will explain the principle, and then illustrate it with a simple calculation.

The principle is to use part of an air conditioning process.

The Stirling engine should be kept warm by the nuclear reactor at all times. (As long as it does not move it will not transfer any - or very little heat.) On the cold side of the engine it should either be an additional heat exchanger or pipes/tubes/channels acting as such where either refrigerants as R134a, R410A, propane, CO2 or other easily evaporated liquids are supplied.

R134a boils at -26°C at atmospheric pressure, R410A at 51.6°C and propane at -42°C. Both R134a and Propane remain liquid at approximately 7 to 8 bar at 30°C, while R410A remains liquid at just under 20 bar at 30°C. CO2 has a melting temperature at -78°C at atmospheric pressure (by sublimation) because it is not in a liquid state under 5 bar pressure. At room temperature CO2 is liquid at just under 50 bar.

The way to “kick start” a Stirling engine is to keep the engine warm, and cool of the cold side at startup by evaporating a refrigerant, Propane or other appropriate liquids. These liquids are kept in a pressurized tank, connected to the cold side of the engine by a valve. After evaporation, the gas will be ventilated to the outside air. In case of propane it should be burned with a catalytic torch.

The calculations are based on a Stirling engine that requires some 100 kW of heat to produce some 25 kW of mechanical power, using a noble gas as a working media.

One can assume that for such engine the cold side consists of some 520 kg of Aluminum.

Further we assume that the cold side should be cooled off 125K (the 520 kg of Aluminum).

This requires some 61MJ, equivalent to 300 kg of R134a being evaporated and further heated to 50oC. If the engine is cooled for 30 sec the cooling power will be 61MJ/30sec = 2MW.

R134a and R410A are strong greenhouse-contributing gases, therefore propane or CO2 can be an option. For more info on R134a and R410A see DuPont internet site:

FilesSpreadsheet with worked examples of different gases

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