# Air resistance: cylindrical rotor in stator with air gap

Hello,

I am currently doing research on the aerodynamic properties of a rotating cylinder in a cylindrical housing.
The cylinder represents a rotor in a electric motor. The air gap between rotor and stator is about 0.5mm.

I'm looking for a theoretical analysis and calculation on the aerodynamical losses in this setup. The rotor will reach speeds up to 25000 rpm

Approximated dimensions:

Rotor diameter: 150 mm
Stator internal diameter: 151 mm

Any help would be highly appreciated.

Kind regards,

Joep

## Answers and Replies

G.I. Taylor performed wide ranging and fundamental studies of this problem. While a fluid mechanics neophyte might be drawn to the laminar flow solution (which is trivial), the rotation of the inner surface leads to large centripetal accelerations of the inner layers of fluid, which unstably break away in structures called Taylor vortices (or taylor gortler structures). The drag is nothing I would care to estimate. In addition, of a myriad vortex structures which can semistably exist, there can be a switch between patterns leading to hysteresis in drag as a function of speed. So to be at all accurate, you really need empirical data relating to your specific geometry and fluid.

Joep van de ven
I misspelled, that's Taylor Goertler