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

Previously reported isothermal linear stability analyses of viscoelastic Ta ylor-Couette flow have predicted transitions to nonaxisymmetric and time-de pendent secondary flows for elasticity numbers E equivalent to De/Re > 0.01 .(1) In contrast, recent experiments by Baumert and Muller(2,3) using const ant viscosity Boger fluids have shown that the primary flow transition lead s to axisymmetric and stationary Taylor-type toroidal vortices. Moreover, e xperimentally 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 thermodyna mically consistent reformulation of the Oldroyd-B constitutive model that t akes into account the influence of thermal history on polymeric stress, and an energy equation that takes into account viscous dissipation effects. Ou r calculations reveal that for experimentally realizable values of Peclet a nd Brinkman numbers, the most dangerous eigenvalue is real, corresponding t o a stationary and axisymmetric mode of instability. Moreover, the critical Deborah number associated with this eigenvalue is an order of magnitude lo wer than those associated with the nonisothermal extensions of the most dan gerous eigenvalues of the isothermal flow. Eigenfunction analysis shows str atification of perturbation hoop stress across the gap width drives a radia l secondary flow. The convection of base state temperature gradients by thi s radial velocity perturbation leads to this new mode of instability. The i nfluence of geometric and kinematic parameters on this instability is also investigated. (C) 1999 American Institute of Physics. [S1070-6631(99)00611- X].