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Rheologica Acta

, Volume 56, Issue 2, pp 73–84 | Cite as

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

  • Hayato MasudaEmail author
  • Takafumi Horie
  • Robert Hubacz
  • Mitsuhiro Ohta
  • Naoto Ohmura
Original Contribution

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.

Keywords

Taylor-Couette flow Shear-thinning fluid Effective Reynolds number Numerical simulation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Hayato Masuda
    • 1
    • 2
    Email author
  • Takafumi Horie
    • 3
  • Robert Hubacz
    • 4
  • Mitsuhiro Ohta
    • 2
    • 5
  • Naoto Ohmura
    • 2
    • 3
  1. 1.School of Food and Nutritional ScienceUniversity of ShizuokaShizuokaJapan
  2. 2.Complex Fluid and Thermal Engineering Research Center (COFTEC)Kobe UniversityKobeJapan
  3. 3.Department of Chemical Science and EngineeringKobe UniversityKobeJapan
  4. 4.Faculty of Chemical and Process EngineeringWarsaw University of TechnologyWarsawPoland
  5. 5.Department of Mechanical Science, Graduate School of Science and TechnologyTokushima UniversityTokushimaJapan

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