Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow

Abstract

The effects of polymer stresses on near-wall turbulent structures are examined by using direct numerical simulation of fully developed turbulent channel flows with and without polymer stress. The Reynolds number based on friction velocity and half-channel height is 395, and the stresses created by adding polymer are modelled by a finite extensible nonlinear elastic, dumbbell model. Both low- (18%) and high-drag reduction (61%) cases are investigated. Linear stochastic estimation is employed to compute the conditional averages of the near-wall eddies. The conditionally averaged flow fields for Reynolds-stress-maximizing Q2 events show that the near-wall vortical structures are weakened and elongated in the streamwise direction by polymer stresses in a manner similar to that found by Stone et al. (2004) for low-Reynolds-number quasi-streamwise vortices (‘exact coherent states: ECS’). The conditionally averaged fields for the events with large contribution to the polymer work are also examined. The vortical structures in drag-reduced turbulence are very similar to those for the Q2 events, i.e. counter-rotating streamwise vortices near the wall and hairpin vortices above the buffer layer. The three-dimensional distributions of conditionally averaged polymer force around these vortical structures show that the polymer force components oppose the vortical motion. More fundamentally, the torques due to polymer stress are shown to oppose the rotation of the vortices, thereby accounting for their weakening. The observations also extend concepts of the vortex retardation by viscoelastic counter-torques to the heads of hairpins above the buffer layer, and offer an explanation of the mechanism of drag reduction in the outer region of wall turbulence, as well as in the buffer layer.

Small scale dynamics of isotropic viscoelastic turbulence

“…Nevertheless, the opposite is observed in some situations, where the energy is transferred from the polymers to the fluid, in particular at small scales. Indeed, a particular mechanism of drag reduction seems to be quite robust: polymers remove energy from vortices [10] when the torque due to the polymer stress is opposed to the rotation of the vortices [21] and polymers release some of their energy close to the wall [10]. Other results from DNS of homogeneous turbulent shear flow [22] were compared to experimental measurements in channel flow and pipe flow [23,24] where it was shown that the average Reynolds shear stress (nonexistent in HIT) and velocity fluctuations perpendicular to the wall are increasingly suppressed when the drag reduction increases.…”

The Polymer Effect on Nonlinear Processes in Decaying Homogeneous Isotropic Turbulence

“…And the polymer additive has the same influence on strong vorticity/strain (self) interaction and has a negative effect on enstrophy production, suggesting that the decrease on enstrophy production is the depression of nonlinearity in DHIT with polymers. That is to say, the negative effect of polymers on enstrophy production (causing the decrease of vortex stretching) in DHIT is similar to a negative torque on vortices as investigated in the polymeric channel flow [13,14].…”

One Equation Model for Turbulent Channel Flow with Second Order Viscoelastic Corrections

“…A 1 À b ð ÞDe l ffiffiffiffiffiffiffi Re l p > À0:5. Research on DNS of channel flow for FENE-P and other differential viscoelastic model fluids [7,11] show viscoelasticity leading to a combination of extra production and dissipation in different regions of the channel: at the edge of the viscous sublayer, there is a small amount of turbulent kinetic energy production, whereas in the log-law region the elasticity is responsible for extra dissipation of k, with the latter being significantly larger than the former. By adopting A=+1 we are thus able to test a situation where P w is everywhere positive and its contribution reduces the production of turbulence.…”

“…These works provide a clear picture of the phenomenon of drag reduction and its relation with the fluid rheology and events, e.g. coherent structure dynamics, taking place in the various regions of the flow [11]. However, from a practical point of view the prediction of the behavior of specific viscoelastic fluids in different turbulent flows remains a challenge, because of the lack of robust turbulent closures to solve the time-averaged momentum and constitutive equations.…”