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This is another attempt at making closed expander cycle a bit more efficient (the first attempt was here). The design combines some elements of both the open and the closed expander cycles (hence the "hybrid") and is briefly described below.

The way I see it, the main potential issue with this design is the heat exchanger. Specifically, I have the following questions:

  • How big a heat exchanger would be needed to cool methane mass flow of 15 kg/s from 400K to 110K? The volume of methane is not too great (15kg at 15 bar is slightly over 2 m^3) - so, it seems like the heat exchanger shouldn't be too big - but would appreciate validation or invalidation of this.
  • What could be a reasonable pressure drop across such a heat exchanger? I've assumed 10 - 15 bar, but not sure if that's too much or too little.

And of course, if there are other issues with this design that I'm not noticing, would appreciate feedback.

Brief description and diagram

The cycle works similarly to the open expander cycle - but instead of discarding turbine exhaust, the exhaust is cooled and pumped back into the engine.

There is a single turbine which drives both the fuel (methane) and the oxidizer pumps. After the fuel goes through its pump, it is split into 2 streams:

  • The first stream is about 20% of the flow. While cooling chamber/nozzle, it is heated up to about 600K and is used to drive the turbine. As it exits the turbine, it goes through a heat exchanger which reduces its temperature from 400K to 110K effectively liquefying the methane. After this, the flow is merged with the flow of methane from the tank, and flows back into the engine.
  • The second stream is the remaining 80% of the fuel. It is also used for cooling the chamber and the nozzle, and is gasified in the process. After this, it is injected into the combustion chamber.

The coolant for the heat exchanger is the subcooled oxygen. As it cools the methane, its temperature rises from 60K to about 120K (though, because of the high pressure, the oxygen remains liquid). It is important to note that even though exit temperature of oxygen is higher than exit temperature of methane, they flow in the opposite directions. So, at all points in the heat exchanger, methane is hotter than oxygen, and thus, heat flows from oxygen to methane. After the oxygen goes through the heat exchanger, it is injected into the combustion chamber.

All the numbers above (and in the diagram below) are directional. I got them doing back-of-the-envelope calculations. I calculated that about 20% of methane flow should be enough to get pressure around 100 bar for the combustion chamber. This 20% should be about 15 kg/s for a Merlin class engine.

enter image description here

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  • $\begingroup$ Your heat exchanger appears to violate the second law of thermodynamics... $\endgroup$ – neph Feb 14 at 3:15
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    $\begingroup$ @neph - do you mean because the exit temp of oxygen is greater than exit temp of methane? If so, I think should be possible with a counter-flow heat exchanger (fluids flow in opposite directions). Specifically, when methane exits at 110K, the oxygen enters at 60K, and when methane enters at 400K, the temperature of oxygen 150K. So, at all point along the heat exchange, temperature of methane is greater than temperature of oxygen. Or is there some other reason which causes the violation? $\endgroup$ – irakliy Feb 14 at 3:36
  • $\begingroup$ I STRONGLY encourage your to determine the enthalpy and entropy of each labeled portion of the flow $\endgroup$ – neph Feb 14 at 3:58
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    $\begingroup$ And also, to mention again, at all points of heat exchange, temperature of methane is greater than temperature of oxygen. So, heat should always flow from methane to oxygen. $\endgroup$ – irakliy Feb 14 at 6:54
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    $\begingroup$ Building lightweight heat exchangers requires high temperature differentials (to drive down exchange area) which should be ok here but it also requires low pressure differentials so the wall thickness can be as thin as possible (problematic here). Moreover it will have a significant pressure drop to ensure good heat transfere due to highly turbulent flow. $\endgroup$ – Christoph Feb 14 at 7:15

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