Experimental observation of the origin and structure of elastoinertial turbulence

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 state of chaotic motion, “elastoinertial 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 qualitative agreement with linear and weakly nonlinear theory. However, in experiments, the dynamics remain weakly chaotic, and the instability can be traced to far lower Reynolds numbers than permitted by theory. For increasing inertia, the flow undergoes a transformation 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.

Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

“…Thus, as shown in Figs 10, 11a and 11b, for both the plane and pipe Poiseuille geometries, the centermode eigenfunction is likely to lead to supercritical nonlinear structures that, either directly, or through secondary instabilities, might underlie the dynamics of the EIT state. The centermode instability, for both pipe and channel flows, therefore provides a continuous pathway from the laminar state to the EIT/MDR regime, a prediction that now has been confirmed in experiments [23]. Beyond the aforementioned range of β, as mentioned above in section 2.3, there exist significant differences between the pipe and plane Poiseuille cases.…”

“…The theoretical predictions are in better agreement with the pipe flow experiments of Chandra et al [83], an aspect that might have to do with the differing methods used to determine the polymer relaxation times in the two efforts. The recent pipe-flow experiments of Choueiri et al [23], however, show excellent agreement between their observations, and theoretical predictions [32,78] for the threshold Re, for E ≤ 0.1. Further, the experiments demonstrate a remarkable match (see Fig.…”

“…While the above instances probed the low Reynolds number (Re) regime where fluid inertial effects are negligible, there have also been many reports of 'early turbulence' in pipe flow of polymer solutions at higher Re, albeit still lower than the oft-quoted Newtonian threshold of Re ∼ 2000 [15,16,17,18,19,20,21]; these early studies were, however, not systematically corroborated in the subsequent literature. In contrast, the recent experiments of Hof and coworkers [22,23], involving pipe flow of polymer solutions at concentrations below or close to the overlap value, have unambiguously demonstrated transition from the laminar state at Re ∼ 1000, thereby confirming the aforementioned observations. The ensuing flow was found to be neither laminar, nor to bear a resemblance to Newtonian turbulence, and was therefore christened 'elasto-inertial turbulence' (EIT) to emphasize the importance of both fluid elasticity and inertia, in contrast to the ET states discussed above.…”

“…This may be seen in the limit Re 1 when the threshold Reynolds number Re c ∝ E −3/2 for both these flows, a scaling that can only be obtained by balancing fluid inertia, elasticity and solvent viscous effects in a thin layer near the pipe centerline/channel midplane [78]; see Figs 8a and 8b. Thus, in sharp contrast to the known irrelevance of linear (modal) stability theory vis-a-vis the Newtonian transition in the canonical shearing flows, a common modal mechanism is predicted to underlie the transition to EIT, in plane-and pipe-Poiseuille flows of an Oldroyd-B fluid, over a significant domain of the Re-W i-β space, with supporting evidence from both simulations [82,87] and experiments [23]. While the center-mode instabilities for pipe-and plane-Poiseuille flows share many similarities, there are crucial differences.…”

“…These novel instabilities can be observed as long as the pipe diameter is small enough (typically a few millimetres), yielding high values of Wi, in which case they exist at Reynolds numbers significantly smaller than the onset of Newtonian turbulence. It is natural to suggest that these instabilities have a purely elastic origin, as was proposed by Samanta et al [22],with their region of existence spreading from Re = 0 to the values observed in early turbulence experiments [24,83,84,23]. A more convincing, yet still indirect, evidence for the existence of sub-critical instabilities in parallel shear flows comes from the phenomenon of melt fracture (mentioned earlier in Sec.…”