[Paper Review] Elastic instability in a straight channel of viscoelastic flow without prearranged perturbations

Yuke Li, Victor Steinberg|arXiv (Cornell University)|Jan 17, 2022

Fluid Dynamics and Turbulent Flows4 citations

TL;DR

This study demonstrates that elastic instability and subsequent elastic turbulence in a straight viscoelastic channel flow can emerge spontaneously from minimal intrinsic perturbations—specifically, a non-smoothed inlet and small pressure holes—without strong prearranged disturbances. The key finding is that self-organized stream-wise streaks and elastic waves persist uniformly across the entire channel length, synchronized by a universal scaling of wave speed with Weissenberg number, resolving the long-standing debate on the necessity of strong external perturbations for instability.

ABSTRACT

We report experimental results on elastic instability in a viscoelastic channel shear flow due to only a natural non-smoothed inlet and small holes along the channel for pressure measurements. We show that non-normal mode instability results in elastic waves and chaotic flow self-organized into periodically cycled stream-wise streaks synchronized by elastic wave frequency. The chaotic flow persists above the transition with increasing $Wi$ further into elastic turbulence and drag reduction regimes. Thus, we resolve the recent puzzle whether strong prearranged perturbations are necessary to get an elastic instability in parallel shear viscoelastic flow. Moreover, flow resistance, velocity spectra decay, and elastic wave speed reveal the same scaling with Wi as obtained in the case of strong disturbances. The remarkable result is that all scaling behavior and streaks are found in the entire channel with small attenuation, in sharp contrast to the flow with strong prearranged perturbations.

Motivation & Objective

• To determine whether elastic instability and turbulent flow in a straight viscoelastic channel can occur without strong prearranged perturbations.
• To investigate whether the scaling laws of flow resistance, velocity spectra, and elastic wave speed observed in strongly perturbed flows also hold under minimal intrinsic perturbations.
• To examine the spatial persistence and dynamics of coherent structures (stream-wise streaks) and elastic waves in the absence of localized disturbance sources.
• To resolve the controversy over whether normal-mode or non-normal-mode instabilities drive elastic turbulence in parallel shear viscoelastic flows.

Proposed method

• Experimental investigation of planar channel flow using a viscoelastic fluid with a non-smoothed inlet and six small holes along the channel for pressure measurements.
• Use of particle image velocimetry (PIV) to measure velocity fields and track coherent structures across the entire channel length.
• Analysis of velocity fluctuation differences (Δu′) at two points across the interface to quantify periodicity of streak dynamics and correlate it with elastic wave cycles.
• Measurement of friction factor, pressure fluctuations, and velocity power spectra to characterize laminar, transitional, elastic turbulence (ET), and drag reduction (DR) regimes.
• Application of non-modal stability analysis principles to interpret the emergence of transient, amplified pseudo-modes from weak initial disturbances.
• Comparison of wave speed scaling with Weissenberg number (Wi) against the critical Wi (Wi_c = 120) to test universality of the scaling relation A(Wi - Wi_c)^δ.

Experimental results

Research questions

• RQ1 Does elastic instability and the resulting chaotic flow emerge in a straight viscoelastic channel flow when only minimal intrinsic perturbations—such as a non-smoothed inlet and small holes—are present?
• RQ2 Do the scaling laws of elastic wave speed, flow resistance, and velocity spectra with Weissenberg number (Wi) remain universal when compared to flows with strong prearranged perturbations?
• RQ3 Are the coherent stream-wise streaks and elastic waves sustained uniformly across the entire channel length in the absence of localized disturbance sources?
• RQ4 Is the periodic cycling of streak dynamics synchronized with the elastic wave frequency, and does this synchronization persist over long distances?
• RQ5 What explains the difference in spatial extent and stability of coherent structures between flows with weak intrinsic perturbations versus strong prearranged disturbances?

Key findings

• Elastic instability and elastic turbulence (ET) occur spontaneously in a straight viscoelastic channel flow due to minimal intrinsic perturbations—specifically, a non-smoothed inlet and six small holes—without any strong prearranged disturbances.
• The elastic wave speed exhibits a universal scaling relation with Weissenberg number: v ∝ (Wi - Wi_c)^δ, with Wi_c = 120, A = 4.5 ± 0.5 × 10^{-3} m/s, and δ = 0.72 ± 0.02, matching results from strongly perturbed flows.
• Stream-wise streaks and elastic waves are self-organized and synchronized by the elastic wave frequency, with a cycling dynamics that repeats periodically over the entire channel length up to l/h = 980.
• Coherent structures and elastic waves persist uniformly across the entire channel with minimal attenuation, in stark contrast to flows with strong perturbations where they decay beyond l/h ≈ 200.
• The absence of secondary instabilities (e.g., Kelvin-Helmholtz-like) in the streaks is attributed to the lower intensity of elastic waves compared to strongly perturbed flows.
• The study resolves the long-standing debate by demonstrating that strong prearranged perturbations are not necessary for elastic instability, as intrinsic non-normal mode instabilities can drive ET via weak initial disturbances.