Drag reduction fundamentals

Abstract

Drag reduction by dilute solutions of linear, random-coiling macromolecules in turbulent pipe flow is reviewed. The experimental evidence is emphasized in three sections concerned with the graphical display of established features of the phenomenon, data correlation and analysis, and the physical mechanism of drag reduction. P. S. VlRK Deportment of Chemical Engineering Indian Institute of TechnologyMadras 600036, India SCOPEOur objective is to acquaint the reader with the phenomenon of drag reduction, in which the skin friction caused by turbulent flow of an ordinary liquid is reduced by additives. This phenomenon, discovered ahnut 1947, has received attention because it suggests practical benefits, such as increased pipeline capacities and faster ships, and is also theoretically stimulating, in the areas of wall turbulence and molecular rheology . This review, restricted to drag reduction by polymer solutions in pipe flow, has three sections: (1) the experimental evidence, (2) correlation and analysis, and (3) mechanism. Section 1 presents experimentally established results showing the flow regimes exhibited by polymer solutions, the relationships among flow and macromolecular parameters, and the changes in mean and turbulent flow structures which accompany drag reduction. The conclusions of Section 1 are documented in Section 2. The latter concerns the empirical correlation of experimental results, with analysis (and tabulations) of the data used for this purpose. Section 2 also provides for discussion of evidence not fully enough established to be included in Section 1. Finally, in Section 3 an attempt is made to physically interpret the experimental results, to infer the nature of the polymer-turbulence interaction responsible for drag reduction and its effect on the energy balances of turbulent pipe flow. CONCLUSIONS AND SIGNIFICANCE1. Gross Flow. Drag reduction by dilute polymer solutions in turbulent pipe flow appears bounded between two universal asymptotes, namely, the Prandtl-Karman law [Equation (2)] for Newtonian turbulent flow and a maximum drag reduction asymptote [Equation (4)]. Between these limits is a polymeric regime in which the observed friction factor relations are approximately linear on Prandtl-Karman coordinates and can be characterized by two parameters-the wall shear stress at the onset of drag reduction and the slope increment by which the polymer solution slope exceeds Newtonian. For a given polymer species-solvent pair: The onset wall shear stress is essentially independent of pipe diameter, polymer concentration, and solvent viscosity, and varies inversely as the two to three power of polymer radius of gyration [Equations (19) and ( 5 ) ] . The slope increment is essentially independent of pipe diameter, varies as the square root of polymer concentration, and as the three-halves power of the number of chain links in the polymer backbone [Equation (S)], and seems unaffected by decreases in polymer excluded volume.2. Mean Velocity Profiles. On law of the wall coordinates, these posse...

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

“…In this regard, measurements of velocity profiles for most polymer solutions showed very good agreement with the 3-layers profile [27], and the solutions used in the present work are indeed among those that were shown to conform to the 3-layers profile. One might then conclude that most polymer solutions should scale well with DR f(V).…”

Turbulent drag reduction using fluid spheres

“…A key property of a drag-reducing particle is a slender shape, a property which is shared by linear polymers (Virk 1975), macroscopic fibres (McComb & Chan 1985), micelles formed by surfactant (Warholic, Scmhidt & Hanratty 1999b) and worm-like agglomerates formed by charged clay particles (Gust 1976). Drag reduction is also observed for spherical solid particles in the gas phase (Rashidi, Hetsroni & Banerjee 1990) and for (nearly) spherical gas bubbles in the liquid phase (Madavan, Deutsch & Merkle 1985).…”

Passive Fields and Particles in Chaotic Flows

“…The second example we consider is the dynamics of long flexible polymers (Lumley, 1969;Virk, 1975). In fluids at rest these polymers are coiled up into tiny spheres.…”

“…Elongated polymers influence the viscosity and change the dynamics on the smallest scales. In the case of turbulent drag reduction these microscopic modifications add up to large scale changes in the velocity field that result in noticeable reductions in drag (Lumley, 1969;Virk, 1975). As a part of a program to understand the effects of polymers on the flow we need to understand the size distribution of the polymers.…”

“…The phenomenon of turbulent drag reduction (Lumley, 1969;Virk, 1975) is connected with the uncoiling of the polymers in the flow. Once uncoiled, the polymers are no longer passive but begin to change the velocity field, so that a reduced drag is observed.…”