very complex problem. it depends on the reynolds number (amoung other factors), whether the cylinder is perfectly immobile and the flexibility of the cylinder.
their are a number of web-site that deal with the phenomena and even have movies of the interaction (experiment and computer simulations).
For agitator in flathead vessels, we are considering using ASTM A108 material. Agitator shaft is used for low speed and low torque service. Can any one comment the suitability of this material. If this is not appropriate material, then suggest a suitable material.