A mechanistic model of turbulent drag reduction by additives

The phenomenon of drag reduction in walled turbulent flows of polymer solutions is theoretically modeled. A new mechanistic model of a polymer molecule in a turbulent flow field is suggested. It is argued that the dominant forces on a polymer fiber in the turbulent flow field are elastic and centrifugal. According to this model, an additional route of dissipation exists, in which eddy kinetic energy is converted to polymer elastic energy by the centrifugal elongation of the rotated polymer, which in turn is viscously damped by the surroundings, when the polymer relaxes. A novel approach is then illustrated, where it is shown that this mechanistic model can be accounted for as a turbulent scale alteration, instead of addition, which enables the classical dimensional analysis of a turbulent boundary layer to apply. Using this dimensional analysis with the equivalent altered scale yields remarkable results. Correct-form velocity profiles are obtained, and Virk's asymptote and slope are predicted with no empirical constants. Drag–flow rate curves are also calculated, and compared favorably with Virk's experiments. The onset of drag reduction phenomenon is also explained by this model, and calculations of it are also compared with Virk's data. The parametric dependencies of the onset point agree well with Virk's conclusions.