[Paper Review] Experimental observation of the origin and structure of elasto-inertial turbulence

George H. Choueiri, José M. López+3 more|arXiv (Cornell University)|Feb 26, 2021

Rheology and Fluid Dynamics Studies31 references48 citations

TL;DR

This study experimentally identifies the origin and structure of elasto-inertial turbulence (EIT) in viscoelastic flows, demonstrating that a linearly predicted chevron-shaped streak pattern emerges near onset, but nonlinear effects dominate earlier than theory predicts. EIT persists across more than three decades of Reynolds number, evolving from a center mode to a wall mode with increasing inertia, and dominates viscoelastic flows up to the maximum drag reduction limit.

ABSTRACT

Turbulence generally arises in shear flows if velocities and hence inertial forces are sufficiently large. In striking contrast, viscoelastic fluids can exhibit disordered motion even at vanishing inertia. Intermediate between these cases, a novel state of chaotic motion, `elasto-inertial turbulence' (EIT), has been observed in a narrow Reynolds number interval. We here determine the origin of EIT in experiments and show that characteristic EIT structures can be detected across an unexpectedly wide range of parameters. Close to onset a pattern of chevron shaped streaks emerges in excellent agreement with linear theory. However, the instability can be traced to far lower Reynolds numbers than permitted by theory. For increasing inertia, a secondary instability gives rise to a wall mode composed of inclined near wall streaks and shear layers. This mode persists to what is known as the `maximum drag reduction limit' and overall EIT is found to dominate viscoelastic flows across more than three orders of magnitude in Reynolds number.

Motivation & Objective

• To experimentally determine the origin and structural evolution of elasto-inertial turbulence (EIT) in viscoelastic shear flows.
• To test the validity of linear stability theory predictions for EIT onset against experimental observations.
• To investigate the transition from early, weakly chaotic flow to fully developed EIT across a wide range of Reynolds numbers.
• To clarify the role of elasticity and inertia in the emergence of EIT, particularly in the context of conflicting stabilization and destabilization effects of polymers.
• To map the persistence of EIT structures from near-threshold instability to the maximum drag reduction regime.

Proposed method

• Conducted experiments using a 50% water-glycerol mixture with 600 ppm polyacrylamide (Mw = 5×10⁶ Da) to achieve high viscosity and viscoelasticity.
• Measured pressure fluctuations and used particle image velocimetry (PIV) to visualize velocity fields in the pipe’s central plane.
• Applied Taylor’s frozen-flow hypothesis to reconstruct time-resolved flow structures from PIV data.
• Performed linear stability analysis on the base laminar flow using the Oldroyd-B model for polymer dynamics and the Hookean dumbbell approximation.
• Solved the dimensionless Navier-Stokes and constitutive equations with finite difference methods on a Gauss-Lobatto-Chebyshev grid, using spectral methods for axial and azimuthal Fourier modes.
• Validated numerical simulations against known results for Newtonian and viscoelastic flows, including critical and unstable cases.

Experimental results

Research questions

• RQ1 Does the experimentally observed flow structure near EIT onset match the least unstable mode predicted by linear stability analysis?
• RQ2 To what extent do nonlinear effects influence the onset of EIT compared to linear theory predictions?
• RQ3 How do EIT flow structures evolve with increasing Reynolds number, particularly from the center mode to the wall mode?
• RQ4 Can EIT structures be detected across a wide range of Reynolds numbers, including the maximum drag reduction regime?
• RQ5 What is the role of polymer elasticity in enabling EIT at Reynolds numbers far below the linear instability threshold?

Key findings

• A chevron-shaped streak pattern, matching the least unstable mode from linear stability analysis, is experimentally observed near EIT onset at Re ≈ 18.
• Nonlinear effects are evident even near threshold, as the flow exhibits fluctuating structures across a range of frequencies, indicating weakly chaotic behavior.
• The elasto-inertial instability persists to Reynolds numbers an order of magnitude lower than predicted by linear theory, suggesting nonlinear destabilization mechanisms.
• As Re increases, the dominant flow structure transitions from a center mode to a wall mode composed of inclined near-wall streaks and shear layers.
• EIT structures persist across more than three orders of magnitude in Reynolds number, extending up to the maximum drag reduction limit.
• The experimental pressure fluctuation amplitude grows approximately with the square root of Re, indicating a continuous increase in turbulent intensity.