True Rotary Vane Engine

Ruf0. I may be wrong.... but.
25 years ago, I worked in Engine Design for a major car company. One of my tasks was to respond to approaches from individuals who had ideas they were looking to sell. One was a supposedly working wooden engine - because he could not make it in metal - that was a large circumference multiple vane engine a almost exactly like yours. When I asked him to explain the pressure difference that developed drive from the high pressure from combustion, he got a friend, a teacher to prepare some calculations - just like your description at comment #11.
But the calculations proved the engine would not work. The pressure difference from a number of chambers opposing sides of different length was innadequate to overcome the friction required for sealing the sliding vanes, when considering the pressure differences across each "power" vane.... and provide adequate torque for the compression phase...
But my 25 year old memory may be wrong?
Curiously, the original patent we found relating to this type of engine was 19th c. And it hasn't ever reached production, despite many people trying. I think Doctor WanKel started from this and developed his engine as a result....
Have you any calculations, or estimates of forces on vanes?
Maybe you'll be the first to make a running engine?
Good luck!
K2

You may want to look at something called the "quasiturbine" .

They have been talking about this wee beastie for probably close to 20 years.
No takes for buying the technology though - - - maybe because it would be fiddly to build - - dunno.
Might get some ideas - - - - dunno - - - - ???

HTH

The Wankel problem is sealing on the side faces and the walls of the chamber that creates the volume change. Thermal expansion of the hot rotor that can not be cooled to the housing temperatures and the vanes will always run hotter still. The "Liquid Piston" (flip of the Wankel) is even worse since the inside of the rotor is the exhaust port. The rotor of a vane engine can have cooling that flows into and out of the rotor so it can have the best cooling possible, least thermal expansion problems, thus tighter clearances.

Understand the the burning of the fuel happens in a short sweep of angle, guess 30 deg. So there will be leakage into the chamber not yet ignited. The leakage will ignite the mixture before it reaches the expansion portion of the sweep. Leakage into the pervious more expanded burned chamber is of no consequence. So the number of vanes is determined by how much pre-ignition is acceptable.

Vane design for sealing, go look at the Wankel seals in detail. If I remember they are three major pieces. to push the smaller seals for the sided outward. This is done by the center vane or the two side vanes being thinner so that it can push on the taper on the side vanes forcing them against the side. Springs and using the high pressure combustion gas to push the van against it's slot to seal that leak path. Alternatively the center vane has 'v' sides and the side seals are two pieces or 'W; shaped with the top of the "W" solid so at that end is the width of the center vane. It is a spring where in the free state the three pieces is wider then the chamber width of the housing. This I believe is the Wankel approach. Springs push the vane against the housing to start. And lubrication of the vane come from the bottom of the slot for each vane. Leakage at the chamber wall is going to happen because the slop relative to the vane changes.

One problem unique to vane engine is the high bending load put on the vane since it sticks out much further then on a Wankel and 'Liquid Piston' engines.

I am sure it is too problematic for almost all.... otherwise we would see production versions of this idea. (I am sure it was around as an idea more than 100 years ago).
K2

Another direct candidate is ASTRON'S OMEGA 1 ENGINE. https://www.slashgear.com/1576972/omega-1-engine-astron-real-everything-need-know/
Still has the three sides to seal and has the same rotors expansion problems The advantage of this engines is the length of the leak paths are very long compared to a van. The only short seal leak path is the rolling contact involute of the gear tooth.

I know this is for an IC engine, but some time ago I was researching rotary vane motors for steam power, and I came across a very in depth research paper where they built a rotary vane steam motor and filled it with sensors. They tried all kinds of vane materials and things like that.

The short story of their result was that you could either lose half your power to leakage, or half your power to friction while trying to make it seal better. However, this type of motor would probably benefit greatly from the square cube rule as leakage loss would decrease as a percentage as it scales up, not that that's useful for model scales.

I did hook a harbor freight pneumatic die grinder up to a boiler once and it worked just as you'd expect.