DYNAMICAL SIMILARITY AND DIMENSIONLESS RELATIONS FOR TURBULENT DRAG REDUCTION BY POLYMER ADDITIVES

Drag reduction in turbulent Bow of high-molecular-weight polymer solut ions has been investigated. Experiments were run in a rotational appar atus with geometrically similar operating units of different sizes. Aq ueous solutions of poly(ethylene oxide) with different molecular weigh ts and solutions of polyisobutylene in kerosene were used. The concent ration and temperature of the solutions were varied. Drag reduction wa s correlated with the rheological characteristics of the solutions; i. e. with the natural time and the shear-thinning viscosity. The dimensi onless viscoelastic parameters have been found, which, with the Reynol ds number, determine the turbulent friction. These are the Weissenberg number and the relative amplitude of the shear-thinning viscosity. Dr ag reduction sets in at a certain value of the local Weissenberg numbe r calculated from turbulent Bow characteristics near the wall. The cri tical value of this criterion is equal to several units. Friction coef ficient versus Reynolds number functions are of a power nature with th e exponent depending on the relative amplitude of the shear-thinning v iscosity. Empirical relations were obtained that can describe fluid fr iction of the polymer solutions in dimensionless form. (C) 1998 Elsevi er Science B.V. All rights reserved.