The interplay of inertia and elasticity in polymeric flows

TL;DR

This study uses direct numerical simulations to explore how fluid inertia and polymer elasticity interact in turbulent flows, revealing complex multiscaling behaviors, energy flux modifications, and differences in dissipation characteristics.

Contribution

It uncovers the combined effects of inertia and elasticity on turbulence dynamics, including multiscaling spectra and energy dissipation, which were not fully understood before.

Findings

Polymeric flows show multiscaling energy spectra dependent on Re and De.

Polymers slow down the nonlinear energy cascade, reducing flux.

Polymer dissipation is less intermittent than fluid dissipation, especially at high elasticity.

Abstract

Addition of polymers modifies a turbulent flow in a manner that depends non-trivially on the interplay of fluid inertia, quantified by the Reynolds number $Re$, and the elasticity of the dissolved polymers, given by the Deborah number $De$. We use direct numerical simulations to study polymeric flows at different $Re$ and $De$ numbers, and uncover various features of their dynamics. Polymeric flows exhibit a multiscaling energy spectrum that is a function of $Re$ and $De$, owing to different dominant contributions to the total energy flux across scales. This behaviour is also manifested in the real space scaling of structure functions. We also shed light on how the addition of polymers results in slowing down the fluid non-linear cascade resulting in a depleted flux, as velocity fluctuations with less energy persist for longer times in polymeric flows. These velocity fluctuations exhibit intermittent, large deviations similar to that in a Newtonian flow at large $Re$, but differ more and more as $Re$ becomes smaller. This observation is further supported by the statistics of fluid energy dissipation in polymeric flows, whose distributions collapse on to the Newtonian at large $Re$, but increasingly differ from it as $Re$ decreases. We also show that polymer dissipation is significantly less intermittent compared to fluid dissipation, and even less so when elasticity becomes large. Polymers, on an average, dissipate more energy when they are stretched more, which happens in extensional regions of the flow. However, owing to vortex stretching, regions with large rotation rates also correlate with large polymer extensions, albeit to a relatively less degree than extensional regions.