Direct numerical simulation of viscoelastic turbulent Taylor-Couette flow
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Since the seminal work of Taylor (1923), the Taylor–Couette (TC) flow has served as a classic paradigm for studies of flow instability and pattern formation as well as turbulence dynamics in both Newtonian and non-Newtonian fluids. For non-Newtonian TC flows, the interactions between fluid elasticity induced by the viscoelasticity and inertia dramatically changed the turbulence dynamics. In order to study the inertio-elastic effects on the TC turbulence, we have performed extensive three-dimensional direct numerical simulations of viscoelastic TC flows over a broad range of 10−4 ≤ Re ≤ 104 and 0 ≤ Wi ≤ 120. Here, the Reynolds number Re and the Weissenberg number Wi are respective dimensionless measures of the inertial and elastic forces. Specifically, the sequence of flow transitions due to a continuous increase of fluid elasticity from classical Newtonian, to inertially and in turn to elastically dominated, and finally to the inertialess purely elastic turbulence, is presented. In each elastically modified turbulent flow state, the drag modification, coherent flow structures, velocity and elastic stress statistics, mechanism of turbulent kineticenergy production, spectral features as well as the self-sustaining cycles of turbulence, are also discussed (see a recent review Song (2023)).