| We investigate the effect of elasticity and thermal gradients on flow instabilities and pattern formation in prototypical curvilinear flows such as Taylor-Couette flows via first principle continuum spectral-based simulations to address various unresolved issues of fluid mechanics that are beneficial to both industry and experimentalists. While it is already known experimentally and theoretically that in the presence of viscous heating, thermally sensitive Newtonian and viscoelastic fluids are prone to thermo-mechanical and thermo-elastic instabilities respectively, a mechanistic model that elucidates the thermo-mechanical instability, and the effect of thermally-induced inertia on the thermo-elastic instability have not been investigated. Secondly, the post-critical dynamics of the viscoelastic Taylor-Couette flow remain largely unexplored. We employ linear stability analysis (LSA) to determine the critical conditions for onset of instabilities and time-dependent nonlinear simulations to investigate the post-critical dynamics. Direct one-to-one comparison with experiments is performed to determine the effect of viscous heating in thermally sensitive Newtonian fluids, and the results are in good agreement depending upon the gap temperature. Using mathematical techniques, scaling laws that govern the thermo-mechanical instability in Dean and Taylor-Couette flows are developed, which are consistent with LSA predictions. It is found that significant destabilization occurs for Newtonian and viscoelastic fluids, when the rotating inner cylinder temperature is higher than that of the stationary outer cylinder by O(1 °C), even in the absence of viscous heating. LSA predictions with varying fluid temperature reveals that thermo-elastic modes can exist at conditions when the flow could no longer be considered purely elastic but inertio-elastic due to thermally-induced reduction in viscosity, which results in O(10) values for Reynolds number. We have developed efficient, 3-dimensional parallel algorithms to explore for the first time, the spatio-temporal pattern formation in Taylor-Couette flow of viscoelastic dilute polymer solutions (isothermal) using dynamical simulations. It is shown that solution structures with varying spatial and temporal symmetries, such as ribbons, flames, disordered oscillations, oscillatory strips and diwhirls, evolve depending on the ratio of fluid relaxation time to the time period of inner cylinder rotation. The flow-microstructure coupling mechanisms underlying the pattern formation process are discussed. |
