Thermomechanical and thermoelastic instabilities in Taylor -Couette flow

In this work, we investigate the stability and dynamics of Taylor-Couette flow of viscous and viscoelastic liquids. Our investigation takes into account the nonlinear thermal transport effects caused by viscous dissipation as well as the complex rheological behavior of the fluids considered. A number of efficient spectral methods has been developed for the numerical simulation of time-dependent and multidimensional viscous and viscoelastic flows during the course of this study to enable the linear and nonlinear bifurcation analyses.;Stability analysis has shown that the use of constitutive models that accurately describe the linear viscoelastic relaxation spectrum of the fluid will provide better quantitative predictions of onset conditions for the flow instability. Moreover, it has been shown that accounting for viscous heating effects will significantly modify the quantitative and qualitative nature of the instability. Specifically, for the first time, new solution families that trigger thermomechanical and thermoelastic instabilities have been uncovered for the Newtonian and viscoelastic Taylor-Couette flows, respectively. Overall, viscous heating effects lead to significant destabilization of the Newtonian and the viscoelastic Taylor-Couette flows that can be attributed to the convection of the base state temperature gradient by the velocity perturbations. This coupling between the energetics and the momentum conservation gives rise to an enhanced centrifugal force in the Newtonian Taylor-Couette flow and to an enhanced hoop stress in the viscoelastic Taylor-Couette flow that significantly reduces the critical shear rate. Our predictions of thermally induced instabilities in Taylor-Couette flow have been experimentally verified by White and Muller (2000a). Unlike the Taylor-Couette flow, viscous heating stabilizes the viscoelastic Dean flow and only modifies the mode selection. These results could have significant implications on the design, optimization and control of the processing of thermally sensitive viscous and viscoelastic fluids. Finally, in order to explore the non-axisymmetric states resulting either from higher order transitions in the non-isothermal flow or primary transitions in the isothermal flow, we have developed computational tools for the simulation of time-dependent and non-axisymmetric viscoelastic Taylor-Couette flow. These simulations have enabled, for the first time, time-dependent and non-axisymmetric simulations of viscoelastic transitions in the Taylor-Couette flow.