Polymer-doped two-dimensional turbulent flow to study the transition from Newtonian turbulence to elastic instability

Abstract

Detecting the flow regimes of Newtonian turbulence (NT), elasto-inertial filament (EIF), elasto-inertial turbulence (EIT), and maximum drag reduction (MDR) of polymer solution and their transition has been a hot topic in the last decade. We attempted to detect NT, EIF, EIT, and MDR by visualizing vortex shedding downstream of an array of cylinders that was inserted perpendicular to polymer-doped two-dimensional (2D) flow. Since polymers are stretched at the cylinders, the consequent vortex shedding is affected by viscoelasticity. The flow regimes are characterized based on Weissenberg (Wi) and Reynolds numbers (Re) with the relaxation time of the polymeric solution estimated from capillary-thinning experiments. The flow regimes are observed for different molecular weights of polyethylene oxide and polyacrylamide in solution and are categorized as either vortex type 1, type 2, and type 3 on a Re–Wi map based on flow visualization using particle image velocimetry. In addition, turbulent statistics of these flow regimes are calculated to more fully quantify these flow regimes. We found that vortex types from 1 to 3 have a similarity to NT, EIF, EIT, and MDR. In addition, characteristic turbulent energy transfer without an increase in turbulent energy production was found in the flow regimes of vortex types 2 and 3 of each polymer solution. Our results suggest intriguing parallels between pipe, jet, and 2D turbulent flow for drag-reducing polymeric solutions.