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Flame lickers work by sucking hot air into a cylinder and then relying on the cooling of the air by the cylinder wall to create a partial vacuum to pull the piston back.

see video

In an alternate time line, could this engine cycle be improved by splitting the intake stroke and the exit stroke between two separate cylinders. The exit stroke would be using a smaller cylinder, and between the cylinders would be an intercooler.

This would increase the surface area which cools the gas* and reduce the repeated heating and cooling the piston and cylinders**.

Or has this engine already been invented?

*the intercooler would have a much larger surface area than the cylinders

**like the early steam engines

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    $\begingroup$ Currently your question is probably going to get closed as off-topic as it is a physics problem and not a worldbuilding one. You could try looking at the Wikipedia article on Sterling engines for more info on the available designs. $\endgroup$ – Rottweiler on market-day. Jun 9 '19 at 7:25
  • $\begingroup$ @DonQualm If the question was modified to include a section asking whether the cylinders could be made from pottery*, and if this could be in reach of a medieval society?; would this be an acceptable question? *as they are sub atmospheric and in compression. $\endgroup$ – Tobe Jun 9 '19 at 15:52
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Essentially you are dealing with fairly primitive hot air engines, and the splitting between two cylinders is similar to early Brayton "Ready Engines". Indeed, atmospheric engines were described by Hero of Alexandria as far back as the First century AD, so this type of technology has a long history.

The limiting factor with any sort of atmospheric engine is there is a hard upper limit to how much power you can produce. Even if you could somehow arrange for a perfect vacuum, the maximum force pushing on the cylinder is 15 PSI (101.325 kPa). You would either need an improbable number of cylinders or really huge ones to generate significant force.

Adding extra stages as you suggest would improve efficiency somewhat, but there would be additional parasitic losses from the extra linkages and the airflow through the cylinders and heat exchangers. Without the actual design it is impossible to calculate how much loss you will get, but at some point it is fairly certain that the losses will outweigh the potential gains. With primitive, hand made machinery this will become a very large effect very quickly.

So while it is possible to build atmospheric engines and add additional stages to increase efficiencies, there will come a point that the extra machinery is actually drawing more power from the engine than it is contributing. Unless there is a very compelling need to gain extra power from the engine, economics suggests that the advantage will go to the most basic engine capable of doing the job, since it will be cheaper to build and operate.

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    $\begingroup$ One thing this design would address is the problem of scaling the flame licker to larger sizes. In the single cylinder original design, the volume of (and heat inside) the cylinder scales with the cube of the size, whereas the area of the cylinder walls only scales with the square. So the ability of the walls to cool the charge of air decreases as the engine grows. $\endgroup$ – Tobe Jun 9 '19 at 20:24

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