Taylor-vortex flow in shear-thinning fluids

Abstract

The present paper deals with the Taylor-Couette flow of shear-thinning fluids. It focuses on the first principles understanding the influence of the viscosity stratification and the nonlinear variation of the effective viscosity µ with the shear rateγ on the flow structure in the Taylor vortex flow regime. A wide gap configuration (η = 0.4) is mainly considered. A weakly nonlinear analysis, using the amplitude expansion method at high order is adopted as a first approach to study nonlinear effects. For the numerical computation, the shear-thinning behavior is described by the Carreau model. The rheological parameters are varied in a wide range. The results indicate that the flow field undergoes a significant change as shear-thinning effects increase. First, vortices are squeezed against the inner wall and the center of the patterns are shifted axially towards the radial outflow boundaries (z = 0, z/λ z = 1). This axial shift leads to increasing concentration of vorticity at these positions. The outflow becomes more stronger than the inflow and the inflow zone, where the vorticity is low, increases accordingly. Nevertheless, the strength of the vortices relative to the velocity of the inner cylinder is weaker. Second, the pseudo-Nusselt number, ratio of the torque to that obtained in the laminar flow, decreases. Third, higher harmonics become more relevant and grow faster with Reynolds number. Finally, the modification of the viscosity field is described.

Shear-thinning mediation of elasto-inertial Taylor–Couette flow

“…The spatial wavelength of the TVF has been found to increase with increased shear-thinning, as observed in experiments and the linear stability analysis by Bahrani et al (2015) (in a large gap flow cell), laser Doppler velocimetry measurements by Escudier et al (1995) or particle image velocimetry (known as PIV) in Cagney & Balabani (2019b). From the two later works and numerical simulations by Topayev et al (2019) and Alibenyahia et al (2012), shear-thinning was found to modify the structure of the Taylor vortices, by making individual vortices asymmetric, and increasing the amplitudes of the travelling waves at the inward and outward jets. Sparse data on the critical Re value for the TVF to WTVF (Bahrani et al 2015;Cagney et al 2020) suggest that the TVF to WTVF transition happens at lower Re values with increased shear-thinning.…”

“…While this analysis has been based on a purely azimuthal CF, the radial viscosity gradient due to the main shear in the gap persists even for higher-order flows. For example in Cagney & Balabani (2019b) and Topayev et al (2019), it is shown that Taylor vortices are squeezed and deform against the inner cylinder, in the lower viscosity inner region (Topayev et al 2019). The previous scaling arguments on enhanced elasticity parameters are thus likely to hold in more complex flows as well due to the base mean shear.…”

“…In shear-thinning fluids with negligible elasticity, the typical transition pattern is 'Newtonian-like': CF-TVF-WTVF (Escudier, Gouldson & Jones 1995;Bahrani et al 2015;Cagney & Balabani 2019b;Topayev et al 2019). In the small gap limit, a decrease in the critical Reynolds number for the formation of Taylor vortices Re TVF experimentally (Escudier et al 1995;Cagney & Balabani 2019a; and numerically (Ashrafi & Khayat 2000;Caton 2006).…”

“…The previous scaling arguments on enhanced elasticity parameters are thus likely to hold in more complex flows as well due to the base mean shear. On the other hand, secondary flows such as Taylor vortices are also affected by shear-thinning (Cagney & Balabani 2019b;Topayev et al 2019), which in turn leads to axial viscosity gradients. Such axial viscosity gradients could well be involved in the damping effect of shear-thinning on transverse elastic waves.…”

“…2015; Cagney & Balabani 2019 b ; Topayev et al. 2019). In the small gap limit, a decrease in the critical Reynolds number for the formation of Taylor vortices (destabilisation) occurs with increased shear-thinning.…”