I think the most important consideration you may have missed, is that the orientation of spinning turbines in the baffle stack would change after every shot, into an infinite variety of combinations. To me, this would make shot to shot velocity and POI shift incredibly inconsistent and completely unpredictable. Might be workable for a sub gun or a bullet hose, but as a precision rifle can, I think it's a non starter. Also, why? You haven't really articulated a particular problem with static baffles your solution would solve.
You bring up an excellent point, but bullet will have exited the suppressor before any movement occurs of the turbines. The orientation of the baffles after each shot is a very insightful point; the use of precision balanced turbines would hopefully render the point moot:; look at the balance of spinning compressors is a jet turbine. I believe that in a precision turbine suppressor stack, the myriad of possible turbine positions would e irrelevant, though I grant you that testing is the only real way to be certain. Furthermore, as to their use in subguns or even rapid fire strings of semiauto fire where the turbines don't come to rest before the next shot, or worse, undergo rotational acceleration as the turbines "spool up" with each successive shot, The suppressor will become less efficient in dampening the sound because less of the expanding gas energy of each successive shot is needed to overcome the inertia of the turbine stack, allowing each successive shot to become louder and louder, although still quieter than the native muzzle blast. Let me add that shot-to shot carbon fouling would probably limit turbine speed, possibly temporarily stopping turbine rotation altogether util the unit is cleaned.
As to why? Look at the goal of suppressor baffles: slowing of the expanding gases, creation of turbulence, and dissipation of the muzzle blast as heat through the exterior walls of the supressor. If the design of open turbines is compared to the average baffle stack, it is evident that turbines would create more turbulence in the same suppressor size. Adding the inertia of movable turbines robs the muzzle gas of more
heat energy as some of that heat is very quickly converted to kinetic energy required to start the turbines turning. Again. in a theoretical sense, a kinetic turbine suppressor should be quieter than a static baffle stack suppressor. However, the problem I am running into is finding a source for he turbines. There does not seem to be a "Turbines R Us" supplier; my google searches so far have led me to a weird maze of Chinese, Indian, and Pakistani websites which I am having a hard time navigating. I'll end this rambling by saying that a kinetic stack turbine may be able to be made smaller to achieve the same noise reduction. All of this depends oon being able to find a readily available source of bearings at a good price point to create an "off the shelf" design that would save time at the lathe turning out baffles.
That's the best answer I can give right now, so I'll see how far I get with this hypothetical design before I proceed or bag it.
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