Common features between the Newtonian laminar–turbulent transition and the viscoelastic drag-reducing turbulence

Abstract

The transition from laminar to turbulent flows has challenged the scientific community since the seminal work of Reynolds (Phil. Trans. R. Soc. Lond. A, vol. 174, 1883, pp. 935–982). Recently, experimental and numerical investigations on this matter have demonstrated that the spatio-temporal dynamics that are associated with transitional flows belong to the directed percolation class. In the present work, we explore the analysis of laminar–turbulent transition from the perspective of the recent theoretical development that concerns viscoelastic turbulence, i.e. the drag-reducing turbulent flow obtained from adding polymers to a Newtonian fluid. We found remarkable fingerprints of the variety of states that are present in both types of flows, as captured by a series of features that are known to be present in drag-reducing viscoelastic turbulence. In particular, when compared to a Newtonian fully turbulent flow, the universal nature of these flows includes: (i) the statistical dynamics of the alternation between active and hibernating turbulence; (ii) the weakening of elliptical and hyperbolic structures; (iii) the existence of high and low drag reduction regimes with the same boundary; (iv) the relative enhancement of the streamwise-normal stress; and (v) the slope of the energy spectrum decay with respect to the wavenumber. The maximum drag reduction profile was attained in a Newtonian flow with a Reynolds number near the boundary of the laminar regime and in a hibernating state. It is generally conjectured that, as the Reynolds number increases, the dynamics of the intermittency that characterises transitional flows migrate from a situation where heteroclinic connections between the upper and the lower branches of solutions are more frequent to another where homoclinic orbits around the upper solution become the general rule.

Turbulence statistics and flow structure in fluid flow using particle image velocimetry technique: A review

“…Velocity gradient is again decreased and the hibernating turbulence state rediscovered. This state is synonymous with reduced viscous stresses thereby increasing the potential for increased perturbation . The similarity between Newtonian laminar‐turbulent transitional flows and drag‐reduced turbulent flows led to the conjecture that viscous effects (Lumley's theory) was more pronounced than elastic effects in the complex mechanism of DR. Other numerical studies have highlighted the important role of polymer elasticity and a description of elastic‐inertia turbulence .…”

“…The recent shift from the traditional view off transition as merely a change from linear to nonlinear dynamics has been shown (by numerical simulation) to extend to viscoelastic drag‐reducing flows. Numerical simulation studies, such as that of have demonstrated interesting similarities between Newtonian laminar‐turbulent transitional flow and drag‐reduced viscoelastic flows, however, there are gaps that can be filled by both numerical simulation and experimental studies (such as PIV technique). These include: Dimensionless parametrization of the common characteristics of these two types of flow. Comparison between both types of flow at similar wall friction (DR). Connection between hibernating turbulence state and high‐DR as well as the active turbulence state and low‐DR. Comparison of the low‐DR and high‐DR limits of both flows.…”

“…The similarity of this characteristic of shear layer thickness and the qualitative effects of DRPs led Zadrazil et al 45 to suggest that there might be a link between shear layer and the underlining mechanism of DR. Similar to Zadrazil et al 45 Graham and coworkers reported a transient characteristic of drag-reduced flow as well as Newtonian fluid flow in their numerical simulation study of the dynamics of turbulent DR. 4,19 They identified two turbulence regimes; hibernating and active turbulence regimes for both Newtonian and drag-reduced flows. The hibernating turbulence regime (which is less frequent in turbulent Newtonian fluid flow compared to drag-reduced flow) showed MDR characteristics such as near-zero Reynolds shear stresses, weak vortices and streamwise streaks.…”

“…Numerical simulation of drag‐reducing flows has also been extended to curved conduits with reasonable success. These include the works of Mompean and coworkers on drag‐reduced flows in straight and curved conduits …”

“…These include the works of Mompean and coworkers on drag-reduced flows in straight and curved conduits. [16][17][18][19]…”