Direct numerical simulation on transition of viscoelasticTaylor-Couette flow

Abstract

Direct numerical simulation has been performed on transition of viscoelastic Taylor-Couette (TC) flow. Specifically, the transition of viscoelastic TC flow starting from the same initial state (AZI) is examined by varying parameters in the following three ways: (1) increasing the inertia while keeping the elasticity unchanged; (2) keeping the elasticity number (a ratio of inertia to elasticity) unchanged while increasing the inertia; (3) keeping the inertia unchanged while increasing the elasticity. The present calculations succeed in reproducing various typical flow states, including rotating standing waves (RSW), axisymmetric oscillatory strip (OS), non-axisymmetric OS and a flow state in form of traveling wave. Interestingly, with the continuously increasing elasticity from OS in Way 3, the OS becomes more turbulent, exhibiting broad PSDs with continuous power-law-decay region. After that, the OS breaks down into a new flow state consisting of intermittent solitary wave (ISW), which is characterized by solitary coherent structure appearing periodically and intermittently in time and localized axially with intense inflow/outflow spot. The transition sequences have been identified for the aforementioned three ways as: (1) from AZI to RSW to strong-weak RSW, then to RSW; (2) from AZI to OS to non-axisymmetric OS, then to a flow state in form of traveling wave; (3) from AZI to OS, then to ISW. On the other hand, three transition pathways which have the same departure and destination in parameter space are examined. Based on comparing the final states (space-time plots and PSDs) of the three pathways, existence of multiple flow states has been confirmed in viscoelastic TC flows.