Abstract
Certain types of macromolecules added to otter and salt solutions flouting in turbulent motion can reduce the pressure gradient. Alternatively, the volumetric capacity of a pipe for these fluids is increased by the presence of these material. Examples presented show that the drag reduction can become significant. Thus, the presence of 0.28 per cent of a gum derivative in a solution of sodium chloride flowing at 200 gal/min in a 1.89- in. pipe yields a pressure drop which is 0.44 of the single-phase drop measured under the same conditions of turbulent flow; the addition of 0.1 per cent of a vinyl derivative to a 1-in. water line yields a through put capacity which is 1.78 of the single-phase capacity at the same pressure drop. It is further shown that these phenomena are distinctly different from previous observations with other classes of non-Newtonian systems. There a simple lowering of friction factors below the levels predicted from the resistance laws for Newtonian fluids is associated with a suppression of turbulent motion. A rational physical explanation for drag reduction is advanced. Briefly, the proposed mechanism is a storage by the molecular elastic elements of the macromolecules in solution of the kinetic energy of the turbulent motion.
Introduction
This study was inspired by a recent review of some paradoxical drag reduction phenomena in turbulent pipe flow. Under very moderate conditions of turbulent flow, the pressure gradient necessary to pump solutions containing certain specific kinds of polymers, fibers and metallic soaps may become appreciably lower than that required to pump the solvent, i.e., water or a low-viscosity hydrocarbon, under identical flow rates in the same conduit. As shown by our review, this phenomenon of drag reduction in turbulent duct flow was first noted during the second world war, apparently arising in connection with the development of flame warfare weapons. Since that time several papers illustrating this phenomenon have appeared: Toms, Oldroyd, Agoston et al., Bundrant and Matthews, Robertson and Mason, Ousterhout and Hall, Daily and Bugliarello, Lummus, Anderson, and Fox. That there are practical applications for techniques which increase discharge or decrease the pressure necessary to transport a liquid through a pipeline is illustrated in the patents which have issued which take advantage of this peculiar phenomenon, e.g., Mysels, Dever, Harbour, and Seifert. One also finds fragmentary evidence of this effect in the data pertaining to a few of the polymeric solutions studied by Shaver and Dodge. However, these investigators were concerned with the development of friction factor vs Reynolds number correlations for a variety of non-Newtonian solutions and suspensions, rather than in a study of drag reduction. A similar kind of drag reduction effect has been observed in gases. Sproull, for example, reports that adding dust to air flowing in turbulent motion through a pipe results in a lowering of the pressure gradient at identical flow rates. There are also military applications for reducing the drag on hydrodynamic vehicles. For example, the possibility of injecting a rheologically complex fluid into the boundary layers of bodies to reduce the skin friction has been investigated by Fabula and Granville. Along somewhat different lines are the drag reduction studies of Kramer. He has shown that skin friction can be reduced by covering the surface of a vehicle with a flexible skin. The effect is apparently due to the boundary layer being stabilized by the presence of the skin. Drag reduction by means of coexisting gas and liquid boundary layers, e.g., film boiling and continuous gas injection, has been proposed by Bradfield, Barkdoll, and Byrne, Cess and Sparrow, Sparrow, Jonsson, and Eckert. Here the skin friction occurs between a vapor and a surface rather than between a liquid and a surface. There are several references in the literature to friction-factor correlations for non-Newtonian solutions and suspensions: Shaver and Merrill, Dodge and Metzner, Clapp, and Thomas.
SPEJ
P. 203ˆ
Calculation Mathod for Velocity and Shear Stress Distribution of Fully Developed Turbulent Pipe Flow Based on Defect Law and Universal Law of Wall and Integrated Turbulence Production.
