Statistics and spectral analysis of turbulent duct flows with flexible and rigid polymer solutions

TL;DR

This study experimentally compares turbulent drag reduction effects of flexible and rigid polymer solutions, revealing similar turbulence suppression mechanisms at comparable conditions and identifying a power-law decay in velocity fluctuation spectra linked to elasto-inertial turbulence.

Contribution

It provides the first detailed comparison of flexible and rigid polymers in turbulent drag reduction, highlighting spectral signatures and the role of polymer concentration in viscoelastic effects.

Findings

Both polymers show similar turbulence effects at comparable drag reduction levels.

Power spectral densities exhibit a -3 slope near the inertial range at high drag reduction.

Flexible polymers are more effective at lower concentrations for drag reduction.

Abstract

We present an experimental investigation of turbulent drag reduction with flexible and rigid polymer solutions. The flexible polymer is partially hydrolyzed polyacrylamide (HPAM) and the rigid polymer is xanthan gum (XG). The experiments are carried out at low drag reduction ($\%DR < 40$), high drag reduction ($\%DR > 40$) and maximum drag reduction (where the velocity profile $U^+$ roughly matches Virk's asymptote). We compare velocity profiles, streamwise and wall-normal Reynolds stresses and power spectra of streamwise velocity fluctuations measured by Laser Doppler Anemometry (LDA). Our results show that the effects of both XG and HPAM polymers on turbulence are similar, provided that the Reynolds numbers and $\%DR$ are also similar. At high levels of $\%DR$, the power spectral densities of streamwise velocity fluctuations of both XG and HPAM flows show a power-law decay near $-3$ instead of $-5/3$ in the inertial range. A slope of the power spectra of $-3$ was recently interpreted as evidence of elasto-inertial turbulence (EIT) in polymer jets. At relatively low concentrations, we observe that flexible polymer solutions are more effective at reducing drag, while XG only reaches MDR at very high concentrations. Thus, we hypothesize that the formation of polymer aggregates with higher concentrations contributes to increase viscoelasticity, and thus $\%DR$, with XG and other rigid polymer solutions.