Oscillating Taylor-Couette Flow

A flow transition in a coaxial rotating cylinder with only inner cylinder rotation was investigated using ultrasonic Doppler method for a wide range of Reynolds number up to 40 times critical Reynolds number (Rc). By analysing spatio-temporal velocity profiles, excitation functions of various transition modes such as wavy and modulated wavy modes were obtained using space-time Fourier expansion (2D-FFT) and Orthogonal Decomposition techniques, and a new fast azimuthal mode was identified and reported. Based on the excitation functions, we reported that the energy supplied in the system by the inner wall is transferred cascading from the Couette flow→Taylor vortex flow (TVF)→Wavy (+Modulated wavy) flow (WVF & MWV)→Fast Azimuthal wavy mode (FAW)→Soft turbulence. Besides the natural sequence of flow transition, it is known that each wavy mode might take an eigenstate of varied eigenvalues of wave number for a fixed geometry. For instance for Taylor Vortex flow, the wave number, namely a cell size, may vary for 0.8 to 1.2 times 2d (d : gap distance). In such a configuration, a spatial forcing is given to the system by setting a wavy wall on the stationary outer cylinder. On the other hand, there has been no attempt to make a forcing on the azimuthal wave. The eignenvalue of WVF (m) may vary from 4 to 7 and the appearance of any m state is a natural sequence. What determines this state is unknown. It is also not known to us if any attempt was made to force the m-state of the WVF or to control the transition sequence. The objective of the present investigation is to see if there is any effect of a perturbation of oscillation of the inner cylinder on the selection of m-state, and if it is possible to control the flow transition or to inject energy directly to any desired wave mode by this means. The experimental configuration is the same (though newly made) as a previously used system (Fig.1); radius of inner cylinder (Ri) is 190 (mm) and outer cylinder (Ro) 210 (mm) and thus the radius ratio η=0.905. The height of the fluid layer (h) is 200 (mm) togive the aspect ratio Γ=20. The inner cylinder is fabricated with FRP to minimize its weight. Measurement is made by ultrasonic Doppler method (UDM) using UVP-X3 (Met-Flow S.A.). The ultrasonic basic frequency was 4MHz and the beam diameter is 4mm∅. The transducer was set at the outside of the gap with its beam center located at 2 mm from the outer wall. Liquid is a water-glycerole mixture. Reynolds number is defined as R=dΩRi/ν (Ω a rotational speed, νkinematic viscosity). A perturbation of oscillation is given by changing the Reynolds number as Fig. 1 Experimental set up. R(t) = Rw + ∆R = Rw (1+Asin(2πf0t)) where f0 is a frequency observed in the power spectrum for the basic WVF and A is an oscillation amplitude to be varied. The experimental procedure is as following; Start up the system for a fixed Reynolds number (Rw=3.0) for WVF mode and measured velocity profiles. Compute a space-averaged power spectrum to find the oscillation frequency f0. Start oscillation of the inner cylinder for a range