Rather than starting with the "easy" standard design, I tried making a 3-piston version described later in West's report, after describing his initial design. Here's my rendition.
I did some analysis of this design. My model sets a displacement for each piston (water column) and temperature for each cylinder (air column). Half of each cylinder is hot, and half is cold. The engine is driven into oscillation because the cylinder isn't centered between these two sides, so sometimes it's heating and sometimes it's cooling. The weight of the pistons acts as restoring force, so assuming they're all of the same length, they have the same resonant frequency. Surprisingly, the cross sectional area of the cylinders and the length of the cylinders doesn't matter in the analysis.
Here is a typical plot of running frequency as a function of the length of the pistons and temperature difference.
The way the engine is supposed to run is that you point a heat gun at the three copper tubes on one side. These are the hot sides of the cylinders, while the others are cold.
The sad part is that while this engine runs beautifully in theory, I could not get mine to start. Keeping the temperature of all cylinders the same is critical or the pistons get out of order, and even with that managed, it never started.
Just to verify that I wasn't completely crazy, I decided to modify the plumbing to make a more standard single piston machine.
I didn't do the analysis of this engine, but it also seemed very unwilling to run unless I flooded the hot cylinders with the pistons.
Under this condition, the tops of the pistons boiled, which raised the pressure substantially. Since the water vapor then condensed on the other (cold) side, the piston didn't boil away completely!
Just to make sure that the fluidyne plumbing wasn't superfluous, I disconnected the plumbing and flooded the hot cylinder on its own.
Here is a video of this test.
You can see the top surface of the cold side of the piston oscillating slightly, but much less than when plumbed. So the fluidyne was "running", even though the boiling seemed very wrong, at least from the original report's description.
However, at this point I recalled reading a rather different design by Morris Dovey. He described a simple prototype that seemed worth trying, at least by modifying the materials I had at hand. Although he claims that his design does not depend on resonant frequencies to run, that is dubious at best. Forced or loaded resonances can vary a bit from their natural frequencies anyway.
I disconnected most of the pipes, added the cold cylinder just hanging off to the side of the hot cylinder, and plugged the cold cylinder with a small screwdriver.
This machine really runs!
It even (sometimes) starts nicely...
But I ran into temperature problems all around, as the clear vinyl tubing is not really able to take the heat from the heat gun. After a minute or so of running, the tubing invariably springs a leak and the machine stops.
I tried flipping the positions of the hot and cold cylinders -- basically just plugging the end of the hot cylinder and leaving a big air bubble below it -- but this did not work. I have not done the analysis of Dovey's design to get a more analytical handle on its operating regimes, but it is still definitely a resonant device. You can feel it try to start running once the heat is sufficient, which is a sure sign that there's a forced resonance.
