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The interplay between viscoelasticity and inertia in dilute polymer solutions at high deformation rates can result in inertioelastic instabilities. The nonlinear evolution of these instabilities generates a state of turbulence with significantly different spatiotemporal features compared to Newtonian turbulence, termed elastoinertial turbulence (EIT). We ex- plore 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 inertioelastic 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 spatiotemporal 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.
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Elasto-Inertial Turbulence
The dissolution of minute concentration of polymers in wall-bounded flows is well-known for its unparalleled ability to reduce turbulent friction drag. Another phenomenon, elasto-inertial turbulence (EIT), has been far less studied even though elastic instabilities have already been observed in dilute polymer solutions before the discovery of polymer drag reduction. EIT is a chaotic state driven by polymer dynamics that is observed across many orders of magnitude in Reynolds number. It involves energy transfer from small elastic scales to large flow scales. The investigation of the mechanisms of EIT offers the possibility to better understand other complex phenomena such as elastic turbulence and maximum drag reduction. In this review, we survey recent research efforts that are advancing the understanding of the dynamics of EIT. We highlight the fundamental differences between EIT and Newtonian/inertial turbulence from the perspective of experiments, numerical simulations, instabilities, and coherent structures. Finally, we discuss the possible links between EIT and elastic turbulence and polymer drag reduction, as well as the remaining challenges in unraveling the self-sustaining mechanism of EIT.
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- Award ID(s):
- 1805636
- PAR ID:
- 10415264
- Date Published:
- Journal Name:
- Annual Review of Fluid Mechanics
- Volume:
- 55
- Issue:
- 1
- ISSN:
- 0066-4189
- Page Range / eLocation ID:
- 675 to 705
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1146/annurev-fluid-032822-025933
