Drag reduction scale-up criteria

Abstract

Available drag reduction correlations are presented and their utility for engineering scale-up to a scale-up from a correlation based on friction velocity and the availability of some turbulent flow data with the process fluid of interest is compared. A further purpose is to investigate the consequences of polymer modification of the mean flow profile in the outer layer. Emphasis is placed on accuracy and ability to portray the drag reducing activity of complex systems. In the case of very dilute polymeric systems in large conduits, very accurate predictions may be needed to assess the performance of a particular additive. Similarly, equations capable of detailed predictions of observed behavior can provide needed insight into the mechanism of drag reduction. Inasmuch as the semi-logarithmic resistance law, e.g., the Seyer and Metzner model of turbulent viscoelastic flow, provides a scale-up criterion significantly more complicated to use than a number of other models, an engineering approximation to this model is described. It is shown that for accurate predictions to be made at modest levels of drag reduction activity, the model must be modified to compensate for thickening of the sublayer.

An improved diameter scaling correlation for turbulent flow of drag-reducing polymer solutions

“…The fact that u à w as the invariant provides better correlation than u à p appears somewhat puzzling at first, given the common belief that the shear stress is the governing phenomenon in the subcritical region [17], and also since the actual solution properties should be more relevant than those of an hypothetical solvent fluid.…”

“…They suggested that, in general, only tubes with diameters larger than 10 mm can be scaled adequately by almost all proposed methods. Interestingly, the Savins and Seyer method [17], which is more empirical (scaling with friction velocity), was singled out in the Hoyt and Sellin analysis as more satisfactory than more complex procedures when scaling between tubes with diameters smaller than 10 mm and the larger ones.…”

“…A number of other authors e.g. Astarita et al [15], Lee et al [16], Savins and Seyer [17], then simplified Whitsitt's procedure by using the solvent friction velocity (u à w ) instead of the solution friction velocity (u à p ). The physical connection between the solvent friction velocity and the actual solution flow is then limited as the wall shear stress in an associated water flow has no direct relationship to the actual wall shear stress in the flow of the drag-reducing solution.…”

Evaluation of Surfactant Drag Reduction Effect in a District Heating System

“…This procedure has the drawback that both variables (DR and u * p ) contain the unknown parameter (τ w ), and an iterative procedure is therefore necessary to predict the DR of the solution. A number of other researchers, for example, Astarita et al [9], Lee et al [10], and Savins and Seyer [11], then simplified Whitsitt's procedure by using the solvent friction velocity (u * w ) instead of the solution friction velocity (u * p ) and proposed "correlate model of DR and u * w ." After that, Schmitt et al [12] proposed two different empirical correlations for surfactants depending upon the shear stress level: DR versus τ w for high stresses and τ w versus V (bulk velocity) for low stresses.…”

Scale effects in polymer solution pipe flow

“…An empirical technique devised by Savins and Seyer (1977), and used with great success in commercial pipelines (Burger et al 1981;Lester 1985) in effect modifies the velocity profile found in small pipes to more resemble that observed in larger pipes.…”