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Published in:
20-12-2016 | Original Contribution
Prediction of onset of Taylor-Couette instability for shear-thinning fluids
Published in: Rheologica Acta | Issue 2/2017
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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.