Exceeding the Asymptotic Limit of Polymer Drag Reduction

Abstract

The drag of turbulent flows can be drastically decreased by adding small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the maximum drag reduction (MDR) asymptote; this asymptote is generally attributed to the dynamics being reduced to a marginal yet persistent state of subdued turbulent motion. Contrary to this accepted view, we show that, for an appropriate choice of parameters, polymers can reduce the drag beyond the suggested asymptotic limit, eliminating turbulence and giving way to laminar flow. At higher polymer concentrations, however, the laminar state becomes unstable, resulting in a fluctuating flow with the characteristic drag of the MDR asymptote. Our findings indicate that the asymptotic state is hence dynamically disconnected from ordinary turbulence.

Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence

“…(At this Re and all Wi considered here, the laminar state is linearly stable.) At still higher Wi, the flow, if seeded with a sufficiently energetic initial condition, becomes turbulent again, with a very low value of f − f lam (consistent with experimental observations of [4] in pipe flow) and a very different structure: i.e. a new kind of turbulence comes into existence.…”

“…While channel flow exhibits a two-dimensional linear instability leading to so-called Tollmien-Schlichting (TS) waves, the critical Reynolds number Re = 5772 is much higher than that observed for transition, so these are not traditionally viewed as playing an important role in Newtonian transition.For flowing polymer solutions under some conditions (low concentration, short polymer relaxation times), transition to turbulence occurs via the usual bypass transition. With further increase in Re, drag reduction sets in, and the flow eventually approaches the so-called maximum drag reduction (MDR) asymptote, an upper bound on the degree of drag reduction that is insensitive to the details of the fluid.Under other conditions, flow transitions directly from laminar flow into the MDR regime, and can do so at a Reynolds number where the flow would remain laminar if Newtonian [2][3][4][5]. Recent experiments and simulations [6][7][8] suggest that turbulence in this regime has structure very different from Newtonian, denoting it as "elastoinertial turbulence" (EIT).…”

“…Recent experiments and simulations [6][7][8] suggest that turbulence in this regime has structure very different from Newtonian, denoting it as "elastoinertial turbulence" (EIT). Choueiri et al [4] experimentally observed that at transitional Reynolds numbers and increasing polymer concentration, turbulence is first suppressed, leading to relaminarization, and then reinitiated with an EIT structure and a level of drag corresponding to MDR. Therefore, there are actually two distinct types of turbulence in polymer solutions, one that is suppressed by viscoelasticity, and one that is promoted.…”

Relaminarization by Steady Modification of the Streamwise Velocity Profile in a Pipe

“…riblets [21], grooves [18], shark-skin surfaces [12], hydrophobic walls [70,60] or by forcing small optimal perturbations [17]. Furthermore, modifications of the fluid employing polymer additives [71,10] and modifications of the flow field by means of honeycombs and screens [43,40]. Additionally, an appropriate streamline geometry obviously has a tremendous influence upon the structure of turbulent wall flows and can help to minimize drag [9].…”

Viscoelasticity-induced pulsatile motion of 2D roll cell in laminar wall-bounded shear flow

“…This flow state was characterized by an energy injection from the additive to flow at medium and small scales. According to another work by Choueiri et al (2018), such two-dimensional structures would appear when the additive concentration exceeds the MDR asymptote, whereas in the regime before the MDR asymptote the streamwise vortices are still observed with hibernating behaviors. These observations imply that the influence of viscoelasticity would be dominant in the EIT and change its role from that for the MDR.…”