The Influence of Polymer Additives on Heat and Momentum Transfer in Turbulent Flows

Turbulent drag reduction by small amounts of high molecular weight linear macromolecules has been an intense area of research for more than 80 years. A quantitative understanding of this incredible phenomenon requires a closure model for the Cauchy stress for a viscoelastic fluid and a closure model for the normalized Reynolds stress, which must be a symmetric and non-negative operator for all turbulent flows in inertial and in non-inertial frames. Unlike the Reynolds stress, the Cauchy stress must be frame invariant inasmuch as the active forces at the molecular scale are assumed to be objective vector fields derived from gradients of thermodynamic scalar potentials. However, turbulent fluctuations at the continuum scale are not objective. Thus, the Reynolds stress is not an objective operator. In this presentation, a recently developed closure for the Reynolds stress is used to explore the impact of polymer additives on the friction factor and the Nusselt number for fully-developed pipe flows. The analysis shows that the finite propagation of mean momentum associated with the Cauchy stress decouples the space-time velocity correlation near the solid/fluid interface. This phenomenon accounts for the onset of drag reduction as well as the maximum extent of drag reduction.