Prediction of onset of Taylor-Couette instability for shear-thinning fluids

Abstract

The definition of Reynolds number (Re) in a Taylor-Couette flow for a shear-thinning fluid is discussed in this paper. Since the shear-thinning property causes spatial distribution of fluid viscosity in a Taylor-Couette flow reactor (TCFR), a method to determine Re by using a numerical simulation is suggested. The effective viscosity (η _eff) in Re was the average viscosity using a weight of dissipation function

$$ {\eta}_{\mathrm{eff}}={\displaystyle \sum_{i=1}^N{\overset{\cdot }{\gamma}}_i^2{\eta}_i\Delta {V}_i}/{\displaystyle \sum_{i=1}^N{\overset{\cdot }{\gamma}}_i^2\Delta {V}_i}, $$

where N is the total mesh number, η _i (Pa·s) is the local viscosity, ${\overset{\cdot }{\gamma}}_i$ (1/s) is the local shear-rate, and ΔV _i (m³) is the local volume for each cell. The critical Reynolds number, Re _cr, at which Taylor vortices start to appear, was almost the same value with the Re _cr obtained by a linear stability analysis for Newtonian fluids. Consequently, Re based on η _eff could be applicable to predict the occurrence of Taylor vortices for a shear-thinning fluid. In order to understand the relation between the rotational speed of the inner cylinder and the effective shear rate that resulted in η _eff, a correlation equation was constructed. Furthermore, the critical condition at which Taylor vortices appear was successfully predicted without further numerical simulation.