On the mechanisms of sheet-like extension structures formation and self-sustaining process in elasto-inertial turbulence

Abstract

The elasto-inertial turbulence (EIT) of viscoelastic fluid is induced by the interaction between elastic instability and flow inertia. The recent discovery of the EIT regime enables new insights into the maximum drag reduction phenomenon of viscoelastic fluid flows and verifies the role of elastic instability in drag-reducing turbulence. In this study, the direct numerical simulation (DNS) of EIT is carried out by using the Oldroyd-B model for the first time. EIT simulations are conducted at a fixed Weissenberg number of 60 with a Reynolds number ranging from 1000 to 6000. Based on the DNS results, the Reynolds stress and elastic stress budgets are analyzed, and the formation of sheet-like structures of polymer extension is confirmed. It indicates that EIT has a complex energy picture. The self-sustaining nature of EIT not only involves the energy transformation from streamwise elastic energy (EE) into turbulent kinetic energy (TKE), but also relies on the energy transformation of wall-normal TKE into EE, which further induces energy absorption of elastic shear stress from the mean motion and the transformation of this energy into streamwise EE. Sheet-like structures reflect the polymer extension characteristics in the streamwise direction. Their formation comes from the wall-normal extension induced by turbulence perturbations, which further generates extra nonlinear elastic shear stress that absorbs energy from the mean motion and eventually forms sheet-like structures. In the self-sustaining cycle, fluid inertia lifts the sheet-like structures of polymer extension, further inducing flow instability.