I am wanting something similar to a turbocharger ... or like a jet engine compressor/turbine.
it will be for a wood stove(outdoor) that i want to force airflow through mostly to increase o2 and to solve for back draft ...
Heated with a small Franklin stove for a few years and learned this:
An exhaust pipe rotating cap (like this) solved the back draft issue (for the most part).
Beyond that, any effort to passively tap the energy in the exhaust air flow (at whatever combustion level) to increase combustion efficiency and/or heat output was an exercise in futility...
That could be used to drive another similar unit on a common axle that acts as a "blower" feeding the air input.
The input route is not critical so some flexible duct could connect back down to the stove air inlet.
The axle could also connect to a small low-friction motor as a "start-up" device.
Whether there would be any benefit at all - I have no idea..
If you want airflow for a fire have you thought about not having motors & power, the system if you could make it work would probably be more efficient if you ducted air down to the fire, or created a vacuum up top, there are gizmo's that already do this.