Dynamics of the helical flow between rotating conical cylinders

The stability of the helical flow in a system of coaxial rotating conical cylinders, the inner one rotating and the outer one stationary was experimentally investigated. The helical flow resulted from a Hopf bifurcation, which occurred only when the acceleration of the inner conical cylinder was smaller than 0.06 rad/s2. When the rotational speed of the inner conical cylinder was increased, the transition to turbulence occurred following a succession of flow states: (i) three-dimensional laminar flow (TDLF), (ii) laminar periodic helical flow (LPHF), (iii) doubly periodic wavy helical flow (DWHF), (iv) weakly turbulent helical flow (WTHF) and (v) fully turbulent helical flow (FTHF). Time series obtained by an electrochemical method permitted the identification and analysis of the fundamental frequencies and their evolutions associated with each time-dependent flow state, using Fourier and wavelet transforms. Phase space analysis revealed the associated attractors constructed from the embedded time series. In the FTHF flow state, the fundamental frequency of the helical flow was observed to have a ratio to the rotational frequency of almost twice that of the one measured in the LPHF regime.