Polymer-Induced Turbulent Drag Reduction: Mechanisms, Governing Parameters, Numerical Modeling, and Emerging Machine Learning Approaches—A Comprehensive Review

This comprehensive review systematically examines the fundamental and contemporary concepts underlying the Toms effect—the phenomenon of turbulent drag reduction (DR) induced by the addition of minute concentrations of high-molecular-weight linear polymers to turbulent flows. The evolution of scientific understanding is traced from the classical studies of the mid-twentieth century to contemporary machine-learning-based approaches. The influence of four key parameters is examined in detail: the dimensionless solvent viscosity ratio β, Reynolds number Re, conformational chain length Lc/MW, and macromolecular relaxation time λ. Polymer concentration C is treated as an independent control variable through which the values of these four parameters are partially determined. The principal physical mechanisms at the molecular and hydrodynamic levels are described. The capabilities of numerical modeling approaches (DNS, LES, and RANS) are critically reviewed, along with promising directions for the application of artificial intelligence. Finally, practical guidelines are proposed for validating and interpreting experimental and numerical drag-reduction data over a broad range of hydrodynamic conditions.