Influence of energetics on the stability of viscoelastic Taylor-Couette flow

U. A. Al-Mubaiyedh, Radhakrishna Sureshkumar, B. Khomami

Research output: Contribution to journalArticle

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Abstract

Previously reported isothermal linear stability analyses of viscoelastic Taylor-Couette flow have predicted transitions to nonaxisymmetric and time-dependent secondary flows for elasticity numbers E≡De/Re>0.01.1 In contrast, recent experiments by Baumert and Muller2,3 using constant viscosity Boger fluids have shown that the primary flow transition leads to axisymmetric and stationary Taylor-type toroidal vortices. Moreover, experimentally observed onset Deborah number is an order of magnitude lower than that predicted by isothermal linear stability analyses. In this work, we explore the influence of energetics on the stability characteristics of the viscoelastic Taylor-Couette flow. Our analysis is based on a thermodynamically consistent reformulation of the Oldroyd-B constitutive model that takes into account the influence of thermal history on polymeric stress, and an energy equation that takes into account viscous dissipation effects. Our calculations reveal that for experimentally realizable values of Peclet and Brinkman numbers, the most dangerous eigenvalue is real, corresponding to a stationary and axisymmetric mode of instability. Moreover, the critical Deborah number associated with this eigenvalue is an order of magnitude lower than those associated with the nonisothermal extensions of the most dangerous eigenvalues of the isothermal flow. Eigenfunction analysis shows stratification of perturbation hoop stress across the gap width drives a radial secondary flow. The convection of base state temperature gradients by this radial velocity perturbation leads to this new mode of instability. The influence of geometric and kinematic parameters on this instability is also investigated.

Original languageEnglish (US)
Pages (from-to)3217-3226
Number of pages10
JournalPhysics of Fluids
Volume11
Issue number11
StatePublished - Nov 1999
Externally publishedYes

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ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

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