Any answers?

In textbook articles dealing with hydrodynamic or hydrostatic fluid film bearings, you will find equations that allow you to model axial leakage through an annulus.

Unfortunately, the flow rate is substantially different between the cases when the shaft is centered in the hole and when the shaft is at its maximum eccentricity, bearing on one side of the hole, and probably different still for the case when the shaft is skewed within the hole, touching on opposite faces at opposite ends of the bearing. I don't recall seeing an analysis of that last case, but it probably exists somewhere.

There's no law that says the air has to flow through the shaft.
Given that you are considering variable angle of attack of the stator blades of a turbine stage, the range of motion of the blade has to be limited to less than 90 degrees, probably a lot less.
So you could feed air through the planar face where the blade root rides against the turbine shell, using a hole in the blade root adjacent the shaft, and a crescent shaped slot in the shell. Perhaps you would need a flange at the blade root to maintain sealing, but there's probably space for one there anyway.

Mike Halloran
Pembroke Pines, FL, USA

Not sure what you're trying to do, but the definition of a "static blade" (vane actually) IS that it does not move (rotate) because its function IS to intercept the exit gas from the previous rotating blade, reverse it (putting that torque to the housing) so that the next stage of the rotating blades receives the exhaust gasses from the static vanes at the expected angle and velocity to extract power into the next rotating stage.

Counter-rotating propeller blades on aircraft have been a long dream, best shown on the long-term success of the Tu-144 (?) Russian prop bombers. And not duplicated by anybody else as well. All other designs failed due to lube oil problems, acceleration and deceleration differences between the two prop's when changing power, noise, vibration, vibration, noise, lube oil problems, fatigue, prop clearances, prop losses into the fuselage, noise, and engine failure.

Not saying it can't be done. It just hasn't been done very often on the "easy" problem of slow airplane props that are not mounted inside a huge casting that is heating and cooling and vibrating.

I did not mean that the vanes rotates ,just like the rotor blades, around the axis of the turbine. I want to rotate them around their axis to have control on the air attack angle on the vanes. This method has been used in many GE gas turbines to control the output shaft speed.

I disagree with your premis: Those type of controllable vanes are common: They ARE use in the gas turbine inlets to control how much air DOES enter the GT. BUT! They are used before the inlet of the GT, they are used at very low air speeds and at almost no differential air pressure across the control vanes.

Your concept is valid, but you are assuming the very high differential pressure and extreme temperatures across the limited number of turbine vanes can be solved. Respectfully, no. The turbine vanes, and the compressor end-stage vanes before the burners, cannot be installed as rotating vanes with the metallurgy and internal gas flow openings and ceramics we have today and we need today.