Prediction of Drag Reduction Based on Coherent Fine Scale Eddies in Turbulence.

Abstract

Prediction method of drag reduction is presented based on the coherent fine scale eddy in turbulence. To estimate the drag reduction efficiency, time scale ratio of drag reducers like surfactants to coherent fine scale eddy is introduced for the near wall turbulence. Key point of this prediction method is the utilization of characteristics of the coherent fine scale eddy in full-developed near wall turbulence before the manipulation of drag reduction. From analysis of DNS data, it is shown that the time scale of the coherent fine scale eddy can be approximated to be 20 η/μrms, 20 νρ/τw0 or 80 νρ/Δp0d. Since the time scale of a drag reducer is considered to be constant under a constant condition, the time scale ratio depends on the time scale of the coherent fine scale eddy. Therefore, the range of drag reduction can be estimated from the characteristics of turbulence before the manipulation of drag reduction. The prediction method is applied for the case of drag reduction by surfactants. The ranges of drag reduction are assembled for different mean velocity and pipe diameter. The effective range for each surfactant mixture is derived and estimation of scale-up effects are shown.