Семинар НУГ: «von Kármán swirling flow between a rotating and a stationary smooth disk»

Precise measurements of the torque in a von Kármán swirling flow between a rotating and a stationary smooth disk in three Newtonian fluids with different dynamic viscosities are reported. The dependence of the normalized torque, called the friction coefficient, on Re is found from measurements. Such dependence is in agreement with result that was predicted theoretically for an infinite, unshrouded, and smooth rotating disk which follows from an exact similarity solution of the Navier-Stokes equations, obtained by von Kármán. An error analysis shows that deviations from the theory can be partially caused by background errors. Measurements of the azimuthal and axial velocity profiles along radial and axial directions reveal that the flow core rotates at V θ /r = 0.22 in spite of the small aspect ratio of the vessel. Thus the friction coefficient shows scaling close to that obtained from the von Kármán exact similarity solution, but the observed rotating core provides evidence of the Batchelor-like solution [Q. J. Mech. Appl. Math. 4, 29 (1951)] different from the von Kármán [Z. Angew. Math. Mech. 1, 233 (1921)] or Stewartson [Proc. Camb. Philos. Soc. 49, 333 (1953)] one.