Spatio-temporal Signatures of Elasto-inertial Turbulence in Viscoelastic Planar Jets

TL;DR

This study investigates how viscoelasticity influences the stability and turbulence characteristics of planar jets, revealing nonmonotonic effects on jet stability and unique spatio-temporal features of elasto-inertial turbulence.

Contribution

It provides experimental insights into the nonlinear dynamics of viscoelastic jets, identifying regimes where elasticity destabilizes or stabilizes the flow and characterizing the turbulence features of EIT.

Findings

Elasticity causes nonmonotonic effects on jet stability.

Shear-layer instability emerges at low elasticity levels.

Increased elasticity merges shear-layer into bulk instability.

Abstract

The interplay between viscoelasticity and inertia in dilute polymer solutions at high deformation rates can result in inertio-elastic instabilities. The nonlinear evolution of these instabilities generates a state of turbulence with significantly different spatio-temporal features compared to Newtonian turbulence, termed elasto-inertial turbulence (EIT). We explore EIT by studying the dynamics of a submerged planar jet of a dilute aqueous polymer solution injected into a quiescent tank of water using a combination of schlieren imaging and laser Doppler velocimetry (LDV). We show how fluid elasticity has a nonmonotonic effect on the jet stability depending on its magnitude, creating two distinct regimes in which elastic effects can either destabilize or stabilize the jet. In agreement with linear stability analyses of viscoelastic jets, an inertio-elastic shear-layer instability emerges near the edge of the jet for small levels of elasticity, independent of bulk undulations in the fluid column. The growth of this disturbance mode destabilizes the flow, resulting in a turbulence transition at lower Reynolds numbers and closer to the nozzle compared to the conditions required for the transition to turbulence in a Newtonian jet. Increasing the fluid elasticity merges the shear-layer instability into a bulk instability of the jet column. In this regime, elastic tensile stresses generated in the shear layer act as an "elastic membrane" that partially stabilizes the flow, retarding the transition to turbulence to higher levels of inertia and greater distances from the nozzle. In the fully turbulent state far from the nozzle, planar viscoelastic jets exhibit unique spatio-temporal features associated with EIT. The time-averaged angle of jet spreading, an Eulerian measure of the degree of entrainment, and the centerline velocity of the jets both evolve self-similarly with distance from the nozzle. The autocovariance of the schlieren images in the fully turbulent region of the jets shows coherent structures that are elongated in the streamwise direction, consistent with the suppression of streamwise vortices by elastic stresses. These coherent structures give a higher spectral energy to small frequency modes in EIT characterized by LDV measurements of the velocity fluctuations at the jet centerline. Finally, our LDV measurements reveal a frequency spectrum characterized by a $-3$ power-law exponent, different from the well-known $-5/3$ power-law exponent characteristic of Newtonian turbulence.