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

详细信息    查看全文

• 作者：Hayato Masuda ; Takafumi Horie ; Robert Hubacz ; Mitsuhiro Ohta…
• 关键词：Taylor ; Couette flow ; Shear ; thinning fluid ; Effective Reynolds number ; Numerical simulation
• 刊名：Rheologica Acta
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：56
• 期：2
• 页码：73-84
• 全文大小：
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Characterization and Evaluation of Materials; Polymer Sciences; Soft and Granular Matter, Complex Fluids and Microfluidics; Mechanical Engineering; Food Science;
• 出版者：Springer Berlin Heidelberg
• ISSN：1435-1528
• 卷排序：56

文摘

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.