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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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Homogeneous turbulence in a random-jet-stirred tank
We report an investigation into random-jet-stirred homogeneous turbulence generated in a vertical octagonal prism-shaped tank where there are jet arrays on four of the eight vertical faces. We show that the turbulence is homogeneous at all scales in the central region of the tank that span multiple integral scales in all directions. The jet forcing from four sides in the horizontal direction guarantees isotropy in horizontal planes but leads to more energy in the horizontal fluctuations com- pared with the vertical fluctuations. This anisotropy between the horizontal and vertical fluctuations decreases at smaller scales, so that the inertial and dissipation range statistics show isotropic behavior. Using four jet arrays allows us to achieve higher turbulence intensity and Reynolds number with a shorter jet merging distance compared to previous facilities with two-facing arrays. By changing the array-to-array distance, the parameters of the algorithm that drives random-jet stirring, and attachments to the exits of each jet, we show that we are able to vary the turbulence scales and Reynolds number. We provide scaling relations for the turbulent fluctuation velocity, integral scale, and dissipation rate, and we show how these scales of motion are primarily determined by the properties of individual jets and the diffusion of their momentum with distance from the nozzles. Finally, we examine the signatures of individual jets in the turbulent velocity spectra and report the conditions under which individual jet flows, not fully mixed with the background turbulence, produce a spectral peak and the corresponding frequency associated with the jet forcing timescale.
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- Award ID(s):
- 2211704
- PAR ID:
- 10497876
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Experiments in Fluids
- Volume:
- 64
- ISSN:
- 0723-4864
- Page Range / eLocation ID:
- 185
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00348-023-03721-9
