Fundamental Physics Underlying Polymer Drag Reduction, from Homogeneous DNS Turbulence with the FENE-P Model

Reduction in surface shear stress in turbulent boundary layers implies suppression of turbulent momentum flux, a large-eddy phenomenon. The physics by which dilute concentrations of long-chain molecules alter large-eddy structure and momentum flux is not well understood. Experiment, however, indicates an essential mix of turbulent velocity fluctuations, polymer molecules, and mean shear. We study the consequences of this essential mix through direct numerical simulation (DNS) of homogeneous shear-driven turbulence with polymer-turbulence interactions modeled using the FENE-P (Finite Extensible Nonlinear Elastic with the Peterlin approximation) representation for polymer stress, and the conformation equation predicted with an advanced hyperbolic solver. Progressive increases in nondimensional polymer relaxation time (Weissenberg number) produce progressive reductions in Reynolds stress concurrent with increasing polymer stretch. The predicted 1-D spectra change with polymer addition consistent with experiment. Polymer-turbulence energy exchange is confined to the large scales, indicating a direct, rather than indirect, effect on the flux-carrying eddies. Polymer-turbulence energy exchange, pressure-strainrate correlations, and polymer-stretch play major roles in the dynamics that underlies the suppression of momentum flux and drag reduction. THE BASIS FOR THE STUDY That polymer added at low concentration to wallbounded turbulent shear flows dramatically reduces wall shear stress is well established experimentally (Lumley 1973, Virk 1975). The specific polymerturbulence interactions that lead to drag reduction also alter turbulence structure, velocity correlations, and momentum flux within the large eddies (Oldaker et al. 1968, Donohue et al. 1972, Luchik & Tiederman 1972, Wei et al. 1992, McComb 1977, Dimitropoulos et al. 1998, 2001, van Doorn et al. 1999, Warholic et al. 1999). Even with recent advances in simulation and measurement of polymer-turbulence drag reduction, the detailed physical mechanisms by which large-eddy turbulent fluxes are suppressed by molecules orders of magnitude smaller in scale are not well defined. The current analysis is intended as a step forward in this direction. A few key experimental and numerical observations underlie our study. Firstly, drag reduction initiates only when the boundary layer is turbulent (Virk 1975), so that to decipher the underlying mechanisms is to decipher the interactions between polymer molecules and turbulent fluctuations that initiate and maintain alteration of the large-scale turbulent eddies, where momentum flux is concentrated. Indeed, drag reduction occurs with dramatic reductions in near-wall Reynolds shear stress (Virk 1971, Luchik & Tiederman 1988, Warholic et al. 1999, Dimitropoulos et al. 2001), implying suppression of normal momentum flux and skin friction. However, drag reduction occurs equally over both rough and smooth surfaces (McNally 1968, Spangler 1969, Virk 1971), so that the essential physics of drag reduction does not involve a viscous sublayer. Furthermore, drag reduction initiates as polymer enters lower inertial wall layer from above or below (Wells & Spangler 1967, McComb & Rabie 1979, 1982), suggesting that the source of the underlying polymer-turbulence dynamics lies within the lower inertial layer, which can be approximated as