Secondary instabilities in Taylor–Couette flow of shear-thinning fluids

The stability of the Taylor vortex flow in Newtonian and shear-thinning fluids is investigated in the case of a wide gap Taylor–Couette system. The considered radius ratio is $\eta = R_1/R_2=0.4$ . The aspect ratio (length over the gap width) of experimental configuration is 32. Flow visualization and measurements of two-dimensional flow fields with particle image velocimetry are performed in a glycerol aqueous solution (Newtonian fluid) and in xanthan gum aqueous solutions (shear-thinning fluids). The experiments are accompanied by axisymmetric numerical simulations of Taylor–Couette flow in the same gap of a Newtonian and a purely viscous shear-thinning fluid described by the Carreau model. The experimentally observed critical Reynolds and wavenumbers at the onset of Taylor vortices are in very good agreement with that obtained from a linear theory assuming a purely viscous shear-thinning fluid and infinitely long cylinders. They are not affected by the viscoelasticity of the used fluids. For the Newtonian fluid, the Taylor vortex flow (TVF) regime is found to bifurcate into a wavy vortex flow with a high frequency and low amplitude of axial oscillations of the vortices at ${Re} = 5.28 \, {Re}_c$ . At ${Re} = 6.9 \, {Re}_c$ , the frequency of oscillations decreases and the amplitude increases abruptly. For the shear-thinning fluids the secondary instability conserves axisymmetry. The latter is characterized by an instability of the array of vortices leading to a continuous sequence of creation and merging of vortex pairs. Axisymmetric numerical simulations reproduce qualitatively very well the experimentally observed flow behaviour.

Multiplicity of states in Taylor-Couette flow of a dense granular gas

Molecular dynamics simulations with a purely repulsive Lennard-Jones potential and a normal damping force is used to simulate the granular flow in the annular region between two differentially-rotating cylinders, called the Taylor-Couette flow. The flow transition from the azimuthally-invariant Circular Couette flow (CCF) to the Taylor-vortex flow (TVF) is studied by increasing the rotation rate (ωi) of the inner cylinder, with the outer cylinder being kept stationary. Multiplicity of states, highlighting the hysteretic nature of the “CCF ↔ TVF” transition, is observed over a wide range of rotation rates. The onset of Taylor vortices is quantified in terms of the maximum radial velocity and the net circulation per vortex.